Obviously, it would be much preferable to do removal as prevention rather than cure. The crisis in question could very well involve nuclear war. But even a D Congress would be reluctant to remove a duly elected president, for fear of voter backlash against this “coup”. The R Congressional leadership has that worry, plus an inertia based on the fact that, demented or not, as long as Trump is president, at least he can sign whatever they get through Congress, AND nominate the right SCOTUS justices. That's what's on the plate today, and concern for today's state of political play crowds out any worry about the crisis Trump might bollix tomorrow, that they can tell themselves the adults in the room will keep him from bollixing too badly anyway.
This understanding of what entrenches Trump suggests the new dynamic our side could introduce to get rid of Trump before he starts a nuclear war, or sends the US into default, or whatever crisis he's going to bollix. Take away this complacency of the Congressional Rs, who are the ones who have to act to get impeachment or the 25th done. Sue, based on Trump's public statements, that he obviously doesn't understand something that he signed, therefore his signature is invalid.
You can't sue to challenge his appt of Gorsuch, for example, at least not as the first step, because there were no rage tweets about the nomination, and even if there were, there is no public policy or mechanics of govt involved in that decision that Trump could have shown that he obviously doesn't understand. Gorsuch is where this effort is going, and endangering the Gorsuch appointment is what gets the Rs to remove him before this gets out of hand, but you can't start with Gorsuch. You sue that his immigration order, for example, wasn't signed by a person who understands what he signed well enough for his signature to indicate his will. If it succeeds, everything Trump has signed or ever will sign, becomes vulnerable to reversal based on the finding of mental incompetence in this first case. This vulnerability will be the motive the Congressional Rs will have to remove Trump. The fact that the vulnerability was created by a court finding that Trump was incompetent to sign something will be cover from political backlash.