That sounds nice in theory however, we need a long-term commitment, not a one-night stand. One of the reasons we are in the situation we are in now is the "tomorrow doesn't matter" cap management style via Loomis from Payton. If he leaves, we do not want a repeat.
It's weird to ask for a long term commitment as a team after dumping a coach only one season into it. Granted, Allen isn't exactly new to all of this. So his is probably considered a unique situation.
As for Payton, it's pretty simple, if Gayle decides she wants Payton back and he wants back in, you work in a healthy extension to both ensure the coach will be around a few years and have leverage if he tries to bolt for another team.
Another general point. Him considering the LA teams is pretty reasonable since it's near where he lives currently. I'd fully expect him to do all due diligence he possibly can before looking at the Saints. And regardless, he has to wait for Allen to be fired anyway. Nothing he can do until that happens.