As for barrel wear...it's possible that that would be higher than for a normal gun, but I'm pretty sure that the rather famous author of that design took that into consideration. (It doesn't seem like SpinLaunch's design is immune to firing wear either, considering the sudden rush of air into a space with hypersonic machinery in motion.)
Starlink’s shape is optimized for it’s launch system, while I doubt spaceX is going to use a competitor anytime soon they would seriously consider sufficient cost savings.
I don't think Quicklaunch would have to suffer significant barrel damage, maybe some fouling that can be cleaned off. The pressures and temperatures required are pretty low, and the required chemistries are pretty tame; it's just the velocities that are high.
As to why not use a gun, barrel damage is probably a deal killer for Quicklaunch and other such designs. Quickly spinning something in a vacuum and letting go should allow for launches roughly as fast as you can pull vacuum. Supporting something like a Starlink constellation seems possible with their design which could be incredibly profitable.