That's pretty much what I do.
Back when I first started playing, though, I DMed and was the one to introduce all of my friends ot the game. I misread the rule about who rolls for damage, and as a result I made all damage rolls for PCs and NPCs. Five years later I realized we weren't playing the standard way and asked my group if they'd like to roll their own damage. I was surprised when they said no. The consensus was that they thought the game would feel less immersive, so we kept happily on as we had been.
One of the things I liked about 3e, was the math was setup so the player could handle the roll (1d20 plus some stuff on yer sheet), and as GM, I kept the AC or DC to myself and simply told them if their number was good enough.
Thus, they did most of the work, and I got to easily keep some secrets. Whereas with THAC0, it was easier to tell the player the AC and let them resolve the whole hit/miss thing.
Now one thing I had done that worked well in dungeon crawls, was to look at all the secret doors and other things that a PC might encounter. I would then roll all the checks ahead of time and note them on the map/room description.
In this way, instead of stopping the game to roll some secret thing and maybe tell the PCs something, I simply told them they notice a secret door IF they had succeeded when I actually did the roll.
The result was removal of the mysterious rolls, and a smoothing out of the narrative for describing the room (as I included the hidden bits if they had passed the check).