Not every weapon is designed to be good in every activity. Some are more rounded than others but TLW is a weapon that is far more specialized for crucible. It has a low magazine size and high rate of fire, which right off the bat isn’t necessarily good for PvE. You’ll likely spend more time reloading than anything else and the only real bonus in PvE is hipfire shots will make it reload slightly faster. Even then you’re usually better off going for precision hits on most ads, since it’ll only one shot body the weakest ones like thrall. It’s dps at close range isn’t to bad but getting that close to more dangerous enemies isn’t always a good idea. It also takes your exotic slot and practically any other handcannon(especially exotics) will be more suited for PvE than this one. I love TLW and use it in most low level PvE activities because it doesn’t matter what I use and it’s good for practice. It’s not made for raids. Blind well, story missions, adventures, patrol, strikes, NF’s you can basically get away with using whatever you want. Hand cannons(primaries in general actually) are often not the strongest options for boss damage. There are some exceptions but generally primaries are used as your workhorse, you generally just kill ads with them. There’s no reason TLW should receive buffed PvE damage because if it did, other primaries should be raised to that level as well. Which would make the buff pointless aside from making primaries stronger. As for the recoil, it’s not as uncontrollable as people say. I’ve been using TLW straight for over a week and find myself using ads more than hip fire nowadays. It just takes more practice than some to control it, simply pull down while you’re firing(100 recoil direction, so it goes straight up). Use it constantly and ads as much as you can, it’s a weapon that’s worth putting some time in to get used to. Just vary the fire rate as needed and practice, practice, practice. I’m on PS4 btw and have around a 1.25 overall kd, so I’m not on PC or some amazing player.

PvE is target practice. Endgame content “requires” specific setups, or following a script. Outside of Raids, use whatever you want.