In order to fix "Bayesian Decision Theory" so that it works in multiplayer games, have it search through strategies for the one that leads to maximum utility, rather than just going action by action. I guess this may be a non-mainstream thing?

Nope, that's definitely a standard thing to do. It's what I was referring to when I said:

We can incorporate notions like planning and value of information by defining U(θ; a) recursively in terms of an identical agent to ourselves who has seen one additional observation (or, if we are planning against an adversary, in terms of the adversary).

However, this doesn't actually work that well, since recursively modeling other agents is expensive, and if the adversary is more complicated than our model can capture, we will do poorly. It is often much better to just not assume that we have a model of the adversary in the first place.

If you "need guaranteed performance," just include that information in the utility function.

There is a difference between "guaranteed performance" and "optimizing for the worst case". Guaranteed performance means that we can be confident, before the algorithm gets run, that it will hit some performance threshold. I don't see how you can do that with a Bayesian method, except by performing a frequentist analysis on it.

Given the rest of your article, it looks like "conflated" could be replaced by "correlated" here. Calling the relationship between ideals and algorithms "conflation" already judges the issue a bit :)

When terminology fails to carve reality at its joints then I think it is fair to refer to it as conflation. If it was indeed the case that ideals mapped one-to-one onto algorithms then I would reconsider my word choice.