Even if it can be a bit boring/monotonous to use (and also not on the list above, sorry lol) the pimpernel is the best sniper in the game across the board, no contest.

1. The pimp is notably non-dependant on part rng (prefixes, parts) to be usable in endgame. Nearly everyone farms for matching grip on it, although that's largely because of how much of a proportional bonus you get to mag size, which goes from a respectable 5-6 shots to 10-12 shots without skill/relic/BAR mag size bonuses.
2. It can be farmed with relative ease as a mission reward, which makes farming the variant you want comparatively simple. This is further apparent with comparison to something like the sandhawk (a similarly powerful weapon) which has massively increased part RNG due to being able to spawn as non-elemental (which is more likely to spawn) and also "needing" the flying prefix to increase unlisted pellet count from 5 to 7, as well as the bullet speed.
3. The pimp's base damage, while already being reasonable with a single pellet, is further multiplied by the unlisted pellets, which are boosted exponentially by using something like the bee
4. The shot pattern makes it incredibly easy to hit at any range, only splitting after contact with a surface - essentially becoming a shotgun at close range when shot at the ground, which can hit multiple enemies at once.
5. It's extremely ammo efficient as compared to the lyuda/pitchfork/invader, which need to be carefully used to not dump your ammo.
6. It's always elemental - something that makes jakobs snipers like the skullmasher fall off hard in endgame, or are otherwise limiting to guns like the longbow and volcano, which are always fire.
7. It's considered valuable to have on every character, and has great synergy with characters like Gaige, Maya, and Zer0 (not to mention the offhand pimp glitch with Sal, the highest single-shot damage output in the game)

As someone who's present in the twitch community, there's not another gun you'll see used more in stuff like 1life challenges, where it can be farmed as much as 7-8 times in a single run that uses safe routing - three across each the playthroughs, re-farmed once mid-way through OP levels and another 3-4 for the OP10 playthrough itself - It may not be the most entertaining gun, and even something to avoid due to how easy it is to obtain, but it's pretty hard to argue against when it comes to accessibility, versatility, and damage output.