It depends, if the opponent you're avoiding needs another paycheck you can starve him out and either use it as negotiating leverage or wait for him to take another fight, then make one of your own right after. You can turn a few months delay into a year really easily and eventually enough fans have moved on and you can just do your thing like you were before the close call. This happens a lot. I also wouldn't put it past any human being to delay doing something unpleasant as long as possible.
I think at this level money isn't such a concern over a few months. I see your point though, and of course at this level, the public outrage thing is all the more true.