This is a terrible sentiment. You need a team and you need someone to lead that team. Having the leader just be a puppet is terrible.
You'll get a dysfunctional cabinet this way, you will get grifting, taking advantage of the puppet showing his face to bad ideas and you will get foreign influence prying on the weak puppet president.
And even if the president is not a puppet and "only weak". We have a government falling apart and in deadlock because of our chancellor being a weak leader in Germany. The only thing holding them together at this point is the fear of them losing power sooner in an early election. All it does is give even further rise to the fascists.
You need a competent leader at the head of the cabinet. And that starts with her or him having their mental capacity.