Doesn't the c-stick in and of itself remove technical depth in the same vein that people argue the removal of l-cancelling does? It automates an action that would otherwise take a collection of 2 simultaneous and decently timed inputs in order to execute otherwise.
The "competitive" players sure do oddly pick and choose.
IMO, the C-Stick is not technically deep. In it's basics, if you are grounded it inputs a smash attack for you, if you are in the air it inputs the directional air for you.
Now, if it did something like L-Cancel aerials or auto shield for you after a smash attack, that would be removing technical depth because that is something you have to input after the move.
The C-Stick is very useful for many AT's. For example in melee, crouch-cancel down smashing or doing up-airs without accidentally using your jump. Sure sure, you can learn to do this without the C-Stick but its a tool that is there and it is there for everyone. What's important is that it is there for everyone and every character to use if they wanted to and most importantly, it is not game breaking.