Honestly, the Grizzco weapons in retrospect, actually aren't that great. Grizzco Blaster and Brella are fast firing sure, but that's all, their kill time and kill efficiency leaves something to be desired or are average at best, better than other weapons in their class, but a lot of shooter just perform better. Grizzco Charger is one I say is just legitimately great because it's an instant charge E-liter. Grizzco Slosher being up there as well because if offers things that no other weapons can.
You say it is good at only killing one given boss... and that's where you're wrong. The thing pieces, infinitely, everywhere you shoot it basically leaves a trail of destruction. Have a line of bosses? Done. Have a line or mobs? Done. Have a teammate you need to revive on the other side of some mobs? Done. Two Grizzco Sloshers on a Griller phase is comically entertaining. It's definitely not a weapon that can stand completely on its own, your teammates are gonna have to compensate for some of its faults, mainly painting base, but the Grizzco Slosher does key things that no other weapon can easily, mainly taking out Flyfish and Steelheads (and basically everything else) without any waiting. That's the key, it can kill most bosses without the need for waiting and can kill clusters in an instant, it just straight on attacks and everything dies. It's a very conservative weapon in terms of when you should attack and ink.
I don't die often either, but if a rotation has less than optimal weapons for dealing with Stealheads, they can simple get out of hand. Mainly on a map like Lost Outpost in conjunction with other gating bosses like Steel Eel or other bosses obstructing the way. As for Drizzlers, if it's just one, it's no big deal, but in situations where you're teammates have been neglecting them and there are 2 or even 3, the DoT can become fairly troublesome, it's less about the attack being telegraphed, but any bit of DoT can push you over the edge out of nowhere.