Honestly , I just clip the 2-3” off the front and not worry about it. It’s a minuscule amount of plastic

If you’re trying to be ultra frugal, yes, you can probably clean it off with a solvent. IPA might work. Goo gone would but introduces all sorts of other contaminants.

Would it really cause problems if it did? I'm thinking if it got into the hotend (especially at the small amounts we're talking about), it would probably just melt into the molten filament and not really cause any issues.

There are "filament filters" that are for keeping foreign materials from getting into the hotend, but they're more for particulate things that won't melt and might clog the nozzle. Tape residue (again, at such small quanties) surely would just flow through with the molten filament and be unnoticeable in the final prints.

Yeah, technically it could, but tape sticks really well to most filament. It is more likely that whatever came out of the nozzle was in a dead zone. The nozzle back bore is drilled with a steeper angle than a typical bit, but it is not so acute that there are no dead zones. Sometimes filament can sit in those zones, cook, and go wonky. It happens more often with high temp filaments like polycarbonate. I run a bit of purging filament with every change and rarely have problems.

I would be more concerned about extruder gear issues with residue over time.

Heads up btw, I've found that a good way to remove sticker residue on comic book bags/boards is to take the peeled sticker and use it to "blot" up the residue. It's possible that may work for you with the filament. Idk about your actual question though, seems like it'd be possible.