I ask the players what they want to play, and guide them towards the most optimized way to emulate that concept. After all, your cool and flavorful idea is a lot more fun to play if the character works.
I encourage people to try different characters, and work with them to make their ideas playable, but I don't like deviating too far from the core rules. For example, one player keeps asking for a pet phoenix. That's not happening.
Yes, but not completely. As a DM, one of my jobs is being the storyteller. So, the players describe what they want to do, and I describe what actually happens. 90% of the time, what I describe lines up with what they wanted. The other 10% of the time, the player's idea breaks the rules of the game in some way, and I have to create a narrative excuse for it not happening.
For example, D&D 5E just doesn't have called shots. They conflict with my interpretation of what "hit points" are, and if called shots are a thing, the archers will just call headshots every time, and go for the instant kill.
So, in my games, called shots chronically get caught in armor, simply graze the target, or otherwise have no effects other than the damage caused by a normal attack roll.
I relish plot twists as much as my players do, so I'm just as thrilled when they do something unexpected as they are when I surprise them. There is a direction I want the game to go, but I am not afraid to let my player's actions find a new route.
I've recently been trying to loosen up even more with my storytelling. I'm slowly transitioning from a very Mass Effect-ish storytelling style (railroads with branching paths) to more open-ended campaigns.