I am Italian, and we get quite pissed when the government issues executive orders (the head of state can't do it), although it happens relatively often. I live in France, and when the president resorted to using them it felt like he was threatening democracy. The US mechanism seems the strongest of the three, and people have considered this a normal thing in a democracy long enough for this to happen.
Executive Orders really aren't that powerful. They can only command the executive branch to do something and are not legislature at all. Trump is certainly proving you can get pretty creative with enforcement to enact terror though, I'd agree to that.
This also creates these weird situations where the courts (or the Supreme Court, at least) says "Well the executive order is just an order, and federal agencies will actually have to implement it, and until we see the specific implementation, gosh, we can't evaluate whether the order is to do an illegal thing, even though it's pretty clear that illegal things will be necessary to implement the order. Maybe they'll find a legal way to do it, who knows? We certainly don't!"
Clown court.