Some trap clubs require steel shot. The Skyway, here, does so. Many of the shooters have shot thousands and thousands of rounds through their guns with no harm.
Very few shoot them through full chokes (and it's not recommended). Most shoot modified, a few Improved Modified and do well with it.
The way to go, with steel in cases where one intends to shoot a lot of rounds is to get a gun with choke tubes. Stick a more open choke in, like modified, and there's no problem.
All that being said, I don't shoot steel. My Perazzis all have fixed chokes, some with barrel work by Wilkinson (the Wayne Novak or Bill Laughridge of shotgun work) and I only have one with choke tubes, a BT-99.
Plus I don't think steel shot breaks targets as well as lead. Yes, I have shot steel for trap at the Skyway, but with an 1100 Trap with choke tubes.
Reloading with steel shot is not really any different than reloading lead but one uses a different, heavier wad.
Bob