Tamaki's character is really bad, yeah. It's like she doesn't even have any purpose in the story except to get thrown into random fanservice situations. The sad thing is that her character actually has the potential to be pretty interesting. Her having idolized Rekka and then been betrayed by him could provide a more personal reason for trying to uncover the truth the Fire Force is hiding.
She was someone who more than anything believed in the system, admired it, desperately wanted to become a part of it, only to find the person who she considered to embody the highest values of that system (Rekka) commit the most horrific crimes imaginable. That'd shake anyone's faith, and it makes sense that Tamaki would join Company 8 to root out the corruption infesting the organization she admired so much.
Given most of Company 8 are driven by pretty straightforward "good guy" motives it'd be interesting to have someone motivated by something more personal like betrayal on the team. She could've been like Akane from Psycho-Pass, struggling to reconcile her innate idealism with growing recognition that the system she serves is deeply corrupt. But the crazy thing is that since Tamaki joined the team, as far as I can recall absolutely none of this has been addressed at all. Like, there hasn't even been a single conversation where somebody asks Tamaki how she's coping with the fact that the lieutenant she idolized tried to brutally murder a bunch of kids, or how that'd shape her convictions for trying to uncover the truth behind human combustion. She just exists to look cute, lose her clothes and vaguely crush on Shinra sometimes.
Given how much potential a character in her position has it is really disappointing Ohkubo decided to go in such an inane direction. I don't even have a problem with fanservice normally, but it should at least make sense and not detract from the story. Tamaki's "curse" makes no sense within the rules of the story (unless you assume the Holy Sol is both real and a pervert whose fixated on making this one girl get naked in improbable situations, I guess) and just serves to squander anything interesting that could've been done with her character in cheap fanservice gags.