> The plane, after I eject, should do something reasonable.

There’s a good chance that it can't, and its not impossible that trying to do something reasonable combined with damage that led to and/or resulted from ejection could make things worse.

> starts broadcasting a mayday?

Great idea for peacetime over the homeland, maybe a very bad idea for military operations over contested or enemy territory.

> crashes into the nearest large body of water?

> attempts to fly itself back to base (we have the technology)?

If either of these are useful in a nontrivial share of ejections (except perhaps the former in conditions where it takes no special effort), then there is a serious problem with the training of the people pulling ejection handles and that needs to be fixed, rendering the action not valuable.

> Why would it be controversial to say "Look, guys, we should decide what the plane does after the pilot ejects. Maybe the best policy is just flying same course and speed until fuel exhaustion, but we should choose this policy, not default into it without consideration."

Because ejection is an action chosen when you can no longer meaningfully say what the plane does in any significant way. That’s the whole purpose. If it it is useful to address this question then you have a bigger problem that you need to urgently fix first.