Once you lose independence of the judiciary system you basically lost the last remaining checks and balances. This is why I never bought into the threat of fascism from Trump. He would have to make similar changes which would never get off the ground. The US system has been shown to work exactly as intended on a number of occasions in the last two months.
The problem is the executive state has grown significantly over the last few decades in the US. But that was hardly unique to Trump.
If anything the main issue is the presidents ability to conduct 'military actions' without congress. That seems like a major risk.
But compared to Turkey the situation is far better in other western states. This is one situation where saying "USA DOES IT TOO!" can't be used to dismiss this out of hand (or EU countries in this case). And even if they did it wouldn't make it a good idea.