Great suggestion(s)!
Given the short form nature of games (1-5 sessions), I opted to design the youxia around a fixed class. Now that said, I don't see why a player couldn't choose to switch their sect (and associated sect ability) through the course of a story. This would give them the starting sect technique(s) and then access to the others!
As for unarmed strikes, it could be an easy case of adding an amendment to the "signature weapon" ability to include their literal body!
On the note of "magic item" equivalents, I've actually written a section on martial arts manuals in the core rulebook manuscript!