1) When runners went from executing the Colosseum spark across half of the room (Halfie) to the full room, people started calling it Full Halfie because it's a good name for the trick and because people can easily understand its meaning. I guess you could also call it " charged Shinespark with precise wall jumps in the previous room to spark the whole length of Colosseum", because those are words with meaning.
Underflow is just a name for the trick. It might've been a mistake at first, but now everyone calls it that way and everyone understands what it standards for.
2) We can take two routes here. First, we could apply your argument against every other major glitch that is restricted - because those would also "be more in-line with the idea of a TAS, regardless of the content that it trivializes" and "because errors in the programming are being taken advantage of". So in this case, we would be watching a 0% run that finishes the game in 10 mins or so by triggering the escape and ignoring every boss.
On the second route, we agree that we want to watch a "run" (running around, killing bosses, getting items, etc.) and restrictions must be made to accommodate for that. I invite you to imagine GT Code didn't actually give Samus +53% items at the end screen, but worked as it does otherwise. Would that glitch (or code) make for an interesting "run"? Would watch Samus kill Kraid, rush to GT and breeze through the game one shooting bosses make for a good low% run?
I think that run is better without it and Underflow, although very different technically from GT Code, does provide the same feel of "rush this glitch and the run is over".
