What have we lost? Nothing

Additionally, the birth scene in RotS when Padmé names the second baby Leia becomes a kick in the teeth for first time viewers. If you watch OT then PT, you already have that information. If you watch PT then OT you don't even know those characters yet. This way it becomes a reveal that follows up on Yoda's "there is another" line and Leia being able to sense Luke with the Force in ESB. It works as well as any version of that reveal possibly could given the framework.

I have my issues with TPM, but if you cut it, you lose a bunch of stuff.

You lose getting to see what Obi-Wan was like as a student.

You lose the scene where Anakin gives Padmé the jappor snippet, which comes back in RotS.

You lose the context that Anakin used to be a sweet kid, and the scene where Shmi tells Qui-Gon that he doesn't know greed! That's an important scene for Anakin's character!

Removing Qui-Gon makes a couple moments in AotC and RotS make no sense.

what does that

someone else shaves the barber (that would make the barber someone who does not shave themself, which would mean the barber shaves them)

the barber shaves themself (this would make the barber someone who shaves themself, which would mean they aren't shaved by the barber)

the barber is shaved by a different barber (a different barber still counts as a person.)

the barber is shaved by a razor and not a person (if this counts as not shaving themself then nobody in this town is being shaved by the barber and this does not actually fit any part of the scenario described)

the barber is a woman (women actually count as people so she still needs to be shaved)

the barber is bald (bald people are people too.)