Well, I agree with your second paragraph as a possible reason, which on its own I think would be enough to make most actual people do ethics.
And while Bob and Frank have clearly distinct moralities, since both of them were created by highly similar circumstances and processes (i.e. those that produce humans brains), it seems very likely that there's more than just one or two things on which they would agree.
As for other reasons to do ethics, I think the part of Frank!morality that takes Bob!morality as an input is usually rather important, at least in a context where Frank and Bob are both humans in the same tribe. Which means Frank wants to know Bob!morality, otherwise Frank!morality has incomplete information with which to evaluate things, which is more likely to lead to sub-optimal estimates of Frank's moral preferences as they would be if Frank had known Bob's true moral preferences.
Frank wants to maximize the true Frank!morality, which has a component for Bob!morality, and probability says incomplete information on Bob!morality leads to lower expected Frank!morality.
If we add more players, eventually it gets to a point where you can't keep track of all the X!morality, and so you try to build approximations and aggregations of common patterns of morality and shared values among members of the groups that Frank!morality evaluates over. Frank also wants to find the best possible game-theoretic "compromise", since others having more of their morality means they are less likely to act against Frank!morality by social commitment, ethical reasoning, game-theoretic reasoning, or any other form of cooperation.
Ethics basically appears to me like a natural Nash equilibrium, and meta-ethics the best route towards Pareto optima. These are rough pattern-matching guesses, though, since what numbers would I be crunching? I don't have the actual algorithms of actual humans to work with, of course.
I think there’s a confusion in our discussions of deontology and consequentialism. I’m writing this post to try to clear up that confusion. First let me say that this post is not about any territorial facts. The issue here is how we use the philosophical terms of art ‘consequentialism’ and ‘deontology’.
The confusion is often stated thusly: “deontological theories are full of injunctions like ‘do not kill’, but they generally provide no (or no interesting) explanations for these injunctions.” There is of course an equivalently confused, though much less common, complaint about consequentialism.
This is confused because the term ‘deontology’ in philosophical jargon picks out a normative ethical theory, while the question ‘how do we know that it is wrong to kill?’ is not a normative but a meta-ethical question. Similarly, consequentialism contains in itself no explanation for why pleasure or utility are morally good, or why consequences should matter to morality at all. Nor does consequentialism/deontology make any claims about how we know moral facts (if there are any). That is also a meta-ethical question.
Some consequentialists and deontologists are also moral realists. Some are not. Some believe in divine commands, some are hedonists. Consequentialists and deontologists in practice always also subscribe to some meta-ethical theory which purports to explain the value of consequences or the source of injunctions. But consequentialism and deontology as such do not. In order to avoid strawmaning either the consequentialist or the deontologist, it’s important to either discuss the comprehensive views of particular ethicists, or to carefully leave aside meta-ethical issues.
This Stanford Encyclopedia of Philosophy article provides a helpful overview of the issues in the consequentialist-deontologist debate, and is careful to distinguish between ethical and meta-ethical concerns.
SEP article on Deontology