Any cats and whatever impede the flow of exhaust gases - by removing them you may get quicker turbo spool up
It used be that tuning turbos to run 'rich' (more fuel) was the safer move, because lean can cause engine knock; although I don't really know how things are nowadays
Your information is out of date like you suspected. The causation is now backwards from what you said.
Some people are removing the cats because they're running super rich tuns that trash the cat fast enough to be a problem. No cat on a vehicle this century restricts anything enough to matter when compared to the the rest of the exhaust system.
Some other people who intend to make so much power that they upsize the whole exhaust system they frequently just don't run a cat because the cat is a restriction compared to the now larger system and tuning it out in the software you already paid for is free and a new cat is expensive.
Interesting. The old belief was 'catback for noise, turboback for power'
I remember reading that some big power Lightnings blew motors when the seasons changed (guessing they tuned in the summer so in the winter it ran lean, but I can't recall).
All of this probably depends on how smart your ECU is...or isn't
It used be that tuning turbos to run 'rich' (more fuel) was the safer move, because lean can cause engine knock; although I don't really know how things are nowadays