Specifically in this one it is more about feeling guilty about the ogFL faith and less about "because this is what supposed to be in the original story), she just can't think of a different solution to help the FL. Usually it is "only the FL can make him happy blah blah he will definitely fall for her blah blah"
I agree that it is annoying though, and in my opinion the only reason they introduced the crown prince was just for that
Imo it only gets annoying when they drag it out even when they both clearly already have feelings for one another. Most ppl would feel like a third party in this situation I think. It'd be weirder if FL was okay with it and decides to steal the ML right away. It'd be a "villainess" origin story. She'd become Trashta 2.0 ╥﹏╥
Everything was so fine until the fl became stubborn on pairing ml and ogfl. Like girl he isn't a toy. He has a thing called brain, he CAN THINK. What the hell even goes on authors' mind when they make fl forcefully meddle like that? So annoying