Ok, but (a) they won't, and (b) if they do, who carries out the actual removal of the president from power? ... oh, right, the executive branch, again. Oops.
If your concerns are only procedural, surely congress could fix that if they cared. If they actually had the vote to impeach they could likely have the voter to either pass new law or amend the constitution to ensure the removal is enforced.
Or we could fix it now, before the Constitutional crisis, which is what we were talking about from the start.
Were we? This chain started with the idea of getting rid of the concept of the president and moving to a parliamentary system. Then it shifted a bit into giving the judicial branch its own law enforcement agency.
Those both risk creating a constitutional crisis, not avoiding one.
Amending the Constitution to create a judicial law enforcement agency would not, in itself, be a Constitutional crisis. Or if you meant that such an agency could then cause one, yeah that could happen in theory, but so could the Executive causing a crisis because the courts don't have an enforcement arm. And to act like the President causing the crisis isn't the more likely scenario in 2025 would be stupifyingly ignorant.