The modern system of prime Ministers where the executive comes from parliament seems to play out better in modern politics.
Yes and no. The problem is that in parliamentary systems like that, if the government has a majority then they're unstoppable. In a system with a president who has some actual authority, or a king who isn't merely a figurehead, the Prime Minister can't just do everything he wants. There still needs to be some negotiation.
On the other hand, the world has a lot of authoritarians in it who wore (and in some cases still are) supported by popular votes. People seem really bad at picking leaders who want to serve out a 4-10 year term, then retire to a cushy life afterwards.