Just one more post off-topic and then I will try to leave the subject alone.
The problem would be: how do we choose a President? If by popular vote, we run the risk of getting a dangerous maverick/extremist/demagogue type like Trump or Farage or possibly worse. After Trump's success, and Brexit, I'm afraid I don't trust the electorate in the way you're theoretically supposed to any more. Call me elitist!
If the President was chosen by the government I don't see how they could not be politically biased? And how else would they be chosen?
If they're somehow meant to put themselves forward then It's the old objection of 'those who seek power are sometimes the least suitable to hold it'. But any President would inevitably be a far more divisive figure than members of the RF, particularly if an election was involved. The only sort of President I would like would be a very boring, serious and highly-regarded judge or academic and they would be unlikely to want the job or to garner popular support.
But for me the biggest argument against making this fundamental change is...it's just unnecessary and would be highly de-stablising at a dangerous and insecure point in our, and world, history. So what if KC has a few nice castles and palaces? I honestly couldn't give a monkey's! Good for him, and I wouldn't swap my life with his for all the tea in China.
I'll try to leave it there, with apologies. But threads are organic things and sometimes they go off on quite reasonable tangents...