I wouldn't say "don't like or don't care about", but there are plenty of things I've owned or own where the fact it's a signature doesn't factor in or is meaningless.
Off the top of my head Jackson Rhoads and Broderick, Schecter Loomis, Jackson Futura (Kip Winger signature model).
As far as the Loomis and Broderick go, i like both players and the bands they played for, but not so much that I would call them favorites. I actually think both players overuse their schtick. Like Nevermore a ton, but Loomis has grown less interesting as time has gone on. As far as the Rhoads go, he's a legendary player and those two Ozzy albums are great, but his playing never really spoke to me that much.
As far as the Kip Winger basses go, I like Winger, I think they have great songs, I think Kip Winger is a musically talented dude, his work with Alice Cooper was great too. However, Kip Winger and his "classically trained male ballerina moves" and lyrical content and male model good looks are at the opposite end of the spectrum from the stuff I try to do. So I don't ever really mention, "This is the semi-obscure Kip Winger sig". If you tell people a bass is a Kip Winger sig, it sort of limits its appeal to certain kinds of music that aren't exactly ultra macho.
ENGL Blackmore is a funny case. Huge fan of Deep Purple, huge fan of Rainbow. But Ritchie Blackmore's general douchery and abandonment of rock music in favor of goofy ren fair cosplay shit don't really endear him to me (or anyone for that matter). Huge fan of the shit he's done (up to '92-'93ish), but don't necessarily want to buy his gear due to other factors.
There aren't a lot of players where I would buy something just because it is associated with someone I am a fan of. Couple exceptions. Steve Harris is a fucking huge one. At the time I bought my first P-Bass Fender didn't offer a Steve Harris signature model. So I went and did my own with modding it to his specs. (Sweetwater didn't offer one with a maple board, so the rosewood is a noticable divergence).
I also got into Ibanez Destroyers because Adrian Smith played them, although not for that long.
I don't really care about sig gear that much. A lot of it just comes off as not really having much staying power. Like, when an artist gets a signature that isn't something they've been using for 20 years+ it comes off as disengenuous. For it to matter it has to be an artist I absolutely love, and they have to have a relationship with that instrument that is so long established it is iconic.
There aren't a ton of artists who actually have that deeply established relationships with a particular model. Steve Harris and the P-bass is an exception. The arctic white and lake placid blue iterations of his Precision with the mirrored aluminum pickguard are fucking legendary.
I mean, there are signature models and then there are models that just have a name tacked on them. ESP/LTDs roster is just like. They are just tacking the name of some player on some new shitty design. The player in question hasn't played guitars with those specs for huge amounts of time. When you look at the Steve Harris P-Bass, it's like, you could look up any Iron Maiden performance from the past three decades and that guitar is there. The connection is iconic. The vast majority of players don't stick with a set of specs long enough for it to be an iconic signature. ESP has shit that is like, the same player will have another signature next year.
James Hetfield is an obvious example. His "signature" models don't have a lot of appeal, because it's like, for the fact it's a signature to matter, I want fond memories of watching him play that guitar on their iconic material. I mean, whether it's a cool guitar or not, that's beside the point (I personally think they are ugly). That's not the style of guitar he played during the AJFA era, that's not the style of guitar he played on The Black Album, that's not the style of guitar he played on Master of Puppets. It's some new thing with zero history with his name attached.