I feel like Fry and Amy's dynamic while refreshing and cute at first could probably go only so far.
Too laidback goofballs encouraging one another's antics is good for a gag but not really plots, Fry and Leela while annoying has a utility of Leela as a straight man to Fry's antics or a stick for Fry to make gestures to prove himself.
The only plots I could imagine for Amy and Fry's relationship are "Amy's Parents fuck with Fry because he's a prospectless loser" but Amy herself doesn't have it in her character to create real conflict with someone like Fry.
Also Fry would probably get jealous every other time he's been confronted by a cheating girlfriend he's been pretty pissed about the situation, unless Amy is a bro who helps him get laid rather leaving him twisting in the wind.
But again why are we supposed to believe Amy is a slut? The only time she even remotely acts like a slut is the Bender gets emotions episode and fucks a dude in her car, which Leela was jealous of and then the episode makes fun of her for fucking Zapp which leaked online.