Hosaka is manly, which is the first prerequisite for being GAR. Theresa is too, but by default, she has to do this in spite of her gender. I'll spare you the details of the show you haven't seen and just say that his "gag" is just to be absurdly manly in a comedic and exaggerated way. No, he's not badass, and he isn't killing people, but that's not what GAR is about. Hosaka isn't a troll vote. Maybe he's a little more popular than he should be, but not a troll vote.
He's climbed a mountain in search of his love. He may look stupid and act in weird manners, but he's quixotic that way, hence QUIXOTIC GAR.
He doesn't have superpowers, but even a punk can't hit him with a punch, he strives for perfection for the woman he adores and is quite sincere.
Also, he climbed a mountain half-naked in winter wearing clogs and carrying ramen.
He may not be a killing machine, but he oozes manliness and GAR. QUIXOTIC GAR!
oh yeah, I also agree that women can be GAR, but powerlevels normally make GAR diluted. And Teresa is filled with powerlevels. I can't sense any "romance" in her the same way I can feel from Hosaka.
Men's romance, mind you, not romantic feelings.
The point is that Hosaka is GAR not for his powerlevels, but other qualities. Although I do think we could trust him to save the day should Minami-ke introduce superdeathrobots about to destroy the entire universe.