Using the term "fan service" doesn't so much imply the fans like it as its sole purpose is for the fans, not to progress the show in some other way. A lot of comedy can be considered fan service in this way as well, they press pause on the plot/action, tell a joke, then continue. This is why not all sexual content gets called "fan service," if a scene contains sexual content but that sexual content furthers the story or something, it usually is accepted.
As for who likes Tamaki, there's definitely a market for fan service. I think the key is communication, if the audience understands it's a fan service show, then it's their choice to watch it or not and they can't complain either way. Fire Force gets such a bad rep because it didn't effectively communicate this, and arguably still doesn't with its inconsistency.