So, like, why can't Schiff interrupt on the basis that Nunes is straight up telling lies
That is part of the GOP intent, to get some sound bytes and ammo to distract from their failing defense and immediately turn the circus onto Schiff. They are fishing for nothing else. Not the truth, just some red meat to feed their base.
The media will also lavish a partisan standoff and plaster the clips everywhere, undermining the intent and content of the testimony. Unengaged viewers will possibly hear about the argument and because our nation is stupid, assume both sides are bad.
Yes it's frustrating, but it's possibly better to let them spew garbage and let them flail, than fall right into their trap. Schiff keeping it professional and using his time wisely to rebut their crap as the closing statement, not to mention allowing the witness to prove them wrong is the best course.