I would say that I'm most sympathetic to consequentialism and utilitarianism (if understood to allow aggregation in other ways besides summation). I don't think it's entirely implausible that the order in which harms or benefits occur can matter, and I think this could have consequences for replacement, but I haven't thought much about this, and I'm not sure such an intuition would be permitted in what's normally understood by "utilitarianism".
Maybe it would be helpful to look at intuitions that would justify replacement, rather than a specific theory. If you're a value-monistic consequentialist, treat the order of harms and benefits as irrelevant (the case for most utilitarians, I think), and you
1. accept that separate personal identities don't persist over time and accept empty individualism or open individualism (reject closed individualism),
2. take an experiential account of goods and bads (something can only be good or bad if there's a difference in subjective experiences), and
3. accept either 3.a. or 3.b., according to whether you accept empty or open individualism:
3. a. (under empty individualism) accept that it's better to bring a better off individual into existence than a worse off one (the nonidentity problem), or or,
3. b. (under open individualism) accept that it's better to have better experiences,
then it's better to replace a worse off being A with better off one B than to leave A, because the being A, if not replaced, wouldn't be the same A if left anyway. In the terms of empty individualism, there's A1 who will soon cease to exist regardless of our choice, and we're deciding between A2 and B.
A1 need not experience the harm of death (e.g. if they're killed in their sleep), and the fact that they might have wanted A2 to exist wouldn't matter (in their sleep), since that preference could never have been counted anyway since A1 never experiences the satisfaction or frustration of this preference.
For open individualism, rather than A and B, or A1, A2 and B, there's only one individual and we're just considering different experiences for that individual.
I don't think there's a very good basis for closed individualism (the persistence of separate identities over time), and it seems difficult to defend a nonexperiental account of wellbeing, especially if closed individualism is false, since I think we would have to also apply this to individuals who have long been dead, and their interests could, in principle, outweigh the interests of the living. I don't have a general proof for this last claim, and I haven't spent a great deal of time thinking about it, though, so it could be wrong.
Also, this is "all else equal", of course, which is not the case in practice; you can't expect attempting to replace people to go well.
Ways out for utilitarians
Even if you're a utilitarian, but reject 1 above, i.e. believe that separate personal identities do persist over time and take a timeless view of individual existence (an individual is still counted toward the aggregate even after they're dead), then you can avoid replacement by aggregating wellbeing over each individual's lifetime before aggregating across individuals in certain ways (e.g. average utilitarianism or critical-level utilitarianism, which of course have other problems), see "Normative population theory: A comment" by Charles Blackorby and David Donaldson.
Under closed individualism, you can also believe that killing is bad if it prevents individual lifetime utility from increasing, but also believe there's no good in adding people with good lives (or that this good is always dominated by increasing an individual's lifetime utility, all else equal), so that the killing which prevents individuals from increasing their lifetime utilities would not be compensated for by adding new people, since they add no value. However, if you accept the independence of irrelevant alternatives and that adding bad lives is bad (with the claim that adding good lives isn't good, this is the procreation asymmetry), then I think you're basically committed to the principle of antinatalism (but not necessarily the practice). Negative preference utilitarianism is an example of such a theory. "Person-affecting views and saturating counterpart relations" by Christopher Meacham describes a utilitarian theory which avoids antinatalism by rejecting the independence of irrelevant alternatives.
Carl, you write that you are “more sympathetic to consequentialism than the vast majority of people.” The original post by Richard is about utilitarianism and replacement thought experiments but I guess he is also interested in other forms of consequentialism since the kind of objection he talks about can be made against other forms of consequentialism too.
The following you write seems relevant to both utilitarianism and other forms of consequentialism:
Even if these other pragmatic considerations you mention would not be removed by having control of Earth, the question remains whether they (together with other considerations) are sufficient to make it suboptimal to kill and replace everyone. What if the likelihood that they are in a simulation is not high enough? What if new scientific discoveries about the universe or multiverse indicate that taking into account agents far away from Earth is not so important?
You say,
I don’t mean that the only way to object to the form of consequentialism under consideration is to stipulate away such things and assume they do not exist. One can also object that what perhaps make it suboptimal to kill and replace everyone are complicated and speculative considerations about living in a simulation or what beings on other planets will do. Maybe your reasoning about such things is flawed somewhere or maybe new scientific discoveries will speak against such considerations. In which case (as I understand you) it may become optimal for the leader we are talking about to kill and replace everyone.
You bring up negative utilitarianism. As I write in my paper, I don’t think negative utilitarianism is worse off than traditional utilitarianism when it comes to these scenarios that involve killing everyone. The same goes for negative vs. traditional consequentialism or the comparison negative vs. traditional consequentialist-leaning morality. I would be happy to discuss that more, but I guess it would be too off-topic given the original post. Perhaps a new separate thread would be appropriate for that.
You write,
In that case the ideology (I would say morality) is not restricted to forms of utilitarianism but also include many forms of consequentialism and views that are consequentialist-leaning. It may also include views that are non-consequentialist but open to that killing is sometimes right if it is done to accomplish a greater goal, and that, for example, place huge importance on the far future so that far future concerns make what happens to the few billion humans on Earth a minor consideration. My point is that I think it’s a mistake to merely talk about utilitarianism or consequentialism here. The range of views about which one can reasonable ask ‘would it be right to kill everyone in this situation, according to this theory?’ is much wider.