Part of my work for Arb Research (https://arbresearch.com/). 

Epistemic Status: I have no scientific background and wrote this after only a couple of days thought, so it is very possible that there is some argument I am unaware of, but which would be obvious to physicists, why a ‘resource-gathering without settlement’ approach to interstellar exploration is not feasible. However, my Arb colleague Vasco Grilo has aerospace engineering expertise, and says he can’t think of any reason why it wouldn’t be feasible in principle. Still, take all this with a large dose of caution. 

Some futurists have considered it likely that, at least absent existential catastrophe in the next few centuries, human beings (or our post-human or machine descendants) will eventually attempt to settle our galaxy.  After all, there are vastly more resources in the rest of the Milky Way than in the Solar system. So we could support far more lives and create much more of anything else we care about, if we make use of stuff out there in the wider galaxy. And one very obvious way for us to make use of that stuff is for us to send out spaceships to establish settlements which make use of the energy of the stars they arrive at. Those settlements could in turn seed further settlements in an iterative process. (This would likely require “digital people” https://www.cold-takes.com/digital-people-faq/#fnref6  given the distances involved in interstellar travel.) 

However, this is not the only way in which we could try to make use of resources outside the solar system. Another way to do so would be to try and gather resources and bring them back to the Solar system without establishing any permanent settlements of either humans or AIs outside the Solar system itself. I think that a government on Earth (or elsewhere in the solar system) might actually prefer gathering resources in this way to space settlements for the following reason:

Impossibility of Interstellar Governance (IIG):   Because of the huge distances between stars, it is simply not possible for a government in the Solar system to exercise long-term effective governance over any space colonies further away than (at most) the closest handful of stars. 

For a powerful, although not completely conclusive, case for this claim see this Medium post: https://medium.com/@KevinKohlerFM/cosmic-anarchy-and-its-consequences-b1a557b1a2e3

Given IIG, no government within the Solar system can be the government of a settlement outside it. Therefore, if a government sets up a colony run by agents in another star system, it loses direct control of those resources. Of course, the government can try and exercise more indirect control over what happens by choosing starting colonists with particular values. But it’s unclear the degree of control that will allow for long-term. 

Meanwhile, a government could try and send a mission to other stars which:

A) Is not capable of setting-up a new self-sufficient settlement, or can be trusted not to do so. 

BUT,

B) is capable of setting up physical infrastructure to extract the system’s energy and resources and bringing them back to the Solar system.
                                                                                                                                                                              This way, a government situated in the Solar system could maintain direct control over how resources are used. In contrast if they go the space settlement route, the government cannot directly govern the settlement. So it has to rely on the idea that if values of the initial settlers are correct, then the settlement will use its resources in the way the government desires even whilst operating outside the government’s control.  

A purely resource-gathering mission without settlement will be particularly attractive to governments if the mission is capable of self-replicating at the destination system, in order to reach further stars. (Of course, settlement missions are also more attractive if they can be iterated in this way.)

Purely resource-gathering missions without settlements do have one very obvious disadvantage. Moving resources back to the Solar system is inevitably going to be a less efficient use of them than making use of them in the system where they are harvested. But it’s easy to imagine a government preferring a high chance of direct control of resources, over more efficient use of these resources by initially ideological aligned but ungovernable agents. 
 

Some further points: 

1. It only makes sense to pursue ‘take resources back to the Solar system’ as a government, if you expect to still be around and able to collect the resources after doing so. So stability in terms of governance in the Solar system makes the resource-gathering strategy more likely.
    
2. Insofar as these things are distinguishable, a settlement strategy is more likely if governments are sending out space missions for broad ideological reasons, like, say, a desire to create as many happy lives as possible, or for humans themselves to experience as much of the universe as possible, first-hand. And a settlement-free resource-gathering strategy is more likely if a government's goal is something like ‘expand your control of power and resources’. Why? Because it’s only if it governs the society making use of the resources the missions gather that a government acquires more power and resources through space missions.So from the perspective of a government with the final goal of acquiring power and resources, ungovernable space settlements are guaranteed to be useless.  In contrast, if all a government cares about is that resources are used for some ideological purpose, direct governance of the people using the resources is not of intrinsic value to you. There is at least some chance that if you found a settlement with the right ideology it will use resources as you desire, even if you do not govern the settlers. 
    
3. However despite the proceeding point, even a government motivated by the desire for a certain broad ideological goal, rather than for direct power and control of resources, *might* feel safer using the less efficient ‘bring resources back to the Solar system’ strategy. They might worry that even if the settlers they send out share their own values right now, they might be more likely to diverge from them in the future than the government itself is.
    
4. Despite the proceeding point, even a government motivated by the desire for a certain broad ideological goal, rather than for direct power and control of resources, *might* feel safer using the less efficient ‘bring resources back to Sol’ strategy. They might worry that even if the settlers they send out share their own values right now, they, or their descendants might diverge from them in the future. (Though note that an ideologically motivated government also has to worry about ideological divergence of their successors within the Solar system itself.) 
    
5. A pure resource gathering strategy has another advantage over a settlement strategy, which is that it prevents there being a bunch of different civilizations out there in the universe with no shared government that might go to war with each other. (The ‘cosmic anarchy’ talked about here: https://medium.com/@KevinKohlerFM/cosmic-anarchy-and-its-consequences-b1a557b1a2e3).
    
6. It is possible of course that both the settlement strategy, and the purely resource-gathering strategy might be tried by different governments (or other organizations.)  Even if the first mission launched is able to capture almost all reachable resources unless a second mission is launched very soon after, there might be multiple competing governments which launch first missions around the same time.
    
7.  One argument (from a government’s perspective) in favor of settlement missions which establish new communities over missions which merely harvest resources and return them to Earth is that settlements can presumably defend themselves better than resource-gathering equipment, at least once a large, technologically advanced community is established at the destination star.  

Relevance for Longtermists: 

1. In thinking about what the future might look like, it’s important to consider cases where most human civilization originated sentient beings remain in the Solar system, even as our civilization makes uses of resources from much further afield. At the very least, an argument is needed to rule such scenarios out before you assume that if we harvest the resources of the stars, a large proportion of our human or artificial descendants will live outside the Solar system. 
    
2. From a point of view which values the creation of sentient beings with happy life, a settlement strategy is, all-things-being equal, preferable to a mere resource gathering strategy, since it uses resources more efficiently, and hence can support a higher number of sentient lives.  (Though this assumes the majority of lives created will be worth-living of course.)  So in the-in my best guess unlikely-event that you can do anything now which affects which strategy is used, it might  be high value to increase the chance that the settlement strategy is used. (Though which strategy has higher expected value from a position on which creating happy lives is good also depends on many other things such as the risk of war between different systems, conditional on such a strategy.)