
I don't think it's that Brett doesn't believe in love, but Brett has been approaching the relationship as an opportunity to enjoy himself while he can, before he will eventually fall in line with whatever expectations his family has for him in regards to a spouse.
Kind of like that convo they had where he said after graduating and quitting football, he'd eat chicken nuggets for a year and let himself get fat, then stop and lose it all.
Hayden even interpreted that convo as applying to their relationship as well, realizing that Brett was expecting it to be temporary, from the weird way Brett responded when Hayden said he'd be the one to drag him to the gym. Hayden realized Brett didn't expect Hayden to still be around at that time.

It depends. I interpreted it as Brett didn't think Hayden would be around or that he's more invested in this relationship. It didn't say anywhere that he has to follow the footsteps of his family. But no omega is ever going to satisfy him. And given he wants rough sex. And possibly to be plowed. But I think he doesn't just gives his ass to just anyone though.
There's a question of whether Brett's "doing too much" when his relationship with Hayden can sometimes seem like a casual fwb agreement. But if you go back to Ch. 5-6 when they're in the library, it was explained that Brett had to go through intensive investigation (stalking) to find someone like Hayden. His obsession stems from his long standing dissatisfaction of his life, the people around him, and the role he's continuously expected to play as the alpha son of a rich and prominent family. Therefore when he finally found Hayden he became the sole thing that allowed him to be and experience the very thing that gave him happiness and the freedom to enjoy sex the way he wants it.
I'm not sure if either Brett doesnt believe in love, or simply sees it as something fleeting so he doesnt see the point in getting invested in something temporary. But its possible that part of his feelings for Hayden may already be love, he just doesn't know it yet.