Are there robustly good and disputable leadership practices?

If I had to suggest something which is both robustly good and disputable, I would suggest this principle:

Focus on minimizing the time between when you have an idea and when your customer benefits from that idea.

Evidence for being robustly good

This principle has a variety of names, as many different industries have rediscovered the same idea.

1. The most famous formulation of this principle is probably as part of the Toyota Production System. Traditional assembly lines took a long time to set up, but once set up, they could pump out products incredibly fast. Toyota decided to change their focus instead towards responding rapidly, e.g. they set a radical goal of being able to change each of their dies in less than 10 minutes.
2. Toyota’s success with this and other rapid response principles inspired a just-in-time manufacturing revolution.
3. These principles were included in lean manufacturing, which has led to a variety of derivatives like lean software development and the lean startup.
4. Another stream of development is in the software world, notably with the publication of the Manifesto for Agile Software Development, which drew from prior methodologies like Extreme Programming.
5. Agile project management is now common in many technical fields outside of software.

This underlying principle, as well as its accoutrements like Kanban boards, can be seen in a huge variety of successful industries, from manufacturing to IT. The principle of reducing turnaround time can be applied by single individuals to their own workflow, or by multinational conglomerates. While it is easier to do agile project management in an agile company, it’s entirely possible for small teams (or even individuals) to unilaterally focus on reducing their turnaround times (meaning that this principle is not dependent on specific organizational cultures or processes).There are also more theoretical reasons to think this principle is robustly good. The planning fallacy is a well-evidenced phenomenon, and it reasonably would lead people to underestimate how important rapid responses are (since they believe they can forecast the future more accurately than they actually can).

Evidence for being disputable

1. Waterfall project management (the antithesis of agile project management) is still quite common.
2. Toyota’s success was in part due to how surprising their approach was (compared to the approach taken by US and European manufacturers).
3. Each industry seems to require discovering this principle anew. E.g. The DevOps Handbook popularized these principles in IT Operations only a few years ago. (It explicitly references lean manufacturing principles as the inspiration.)
4. The planning fallacy and other optimism biases would predict that people underestimate how important it is to respond rapidly to changes.

Other candidates

Some other possible principles which are both robustly useful and disputable:

1. Theory of Constraints. This seems well evidenced (the principle is almost trivial, once stated) and managers are often surprised by it. However, I’m not sure it’s really “disputable” – it is more a principle that is unequivocally true, but hard to implement in practice.
2. “Minimize WIP”. This principle is disputable, and my impression is that certain areas of supply chain management consider it to be gospel, but I'm not sure how solid the evidence base for it is outside of SCM. Anecdotally, it's been pretty useful in my own work, and there are theoretical reasons to think it's undervalued (e.g. lots of psychological research about how people underestimate how bad distractions are).
3. Talk to your customers a lot. Popularized by The Four Steps to the Epiphany and then later The Lean Startup. Well regarded among tech startups, but I’m less clear how useful it is outside of that.

Appendix: Evidence From India

One of the most famous experiments in management is Does management matter? Evidence from India. This involved sending highly-paid management consultants to randomly selected textile firms in India. The treatment group had significant improvements relative to the control group (e.g. 11% increase in productivity).How did they accomplish these gains? Through changes like:

1. Putting trash outside, instead of on the factory floor
2. Sorting and labeling excess inventory, instead of putting it in a giant heap
3. Doing preventative maintenance on machines, instead of running them until they break down

I think the conclusion here is that “disputable” is a relative term – I doubt any US plant managers need to be convinced that they should buy garbage bins. Most of the benefits that the management consultants were able to provide were simply in encouraging adherence to (what managers in the US consider to be) “obvious” best practices. Those best practices clearly were not “obvious” to the Indian managers.

only principles which are both robustly good and disputable seem worth teaching

This sounds false to me: You might think different kinds of principles work better and worse for different people's styles, and lots of principles are non-obvious. In that case, it seems worth someone learning about a tonne of different principles and testing out to see if they help or hinder their personal style of management.