I don't think it's just Dick/Babs that bring out the worst in each other. Did Dick and Kory ever have long term prospects? If we read the NTT run (the height of their romance in the comics), it was very important for that stage of their lives but doesn't seem built to last. Dick would close himself off emotionally, Kory would alternate between being reasonable in trying to get him to talk and being incapable of understanding why he won't open up and not give him space. He would unintentionally patronize her and make her feel stupid for not understanding Earth customs and worried she'd fly off the handle and kill people. Donna, who loved them both, warned Kory against living only for Dick and felt Kory was only in love with the idea of them being a couple, not feeling actual love itself. But this didn't pan out and she got together with Dick anyway. At least until she got mad at Dick for being raped by Mirage and then he got creepily possessive of her and they almost got married. Demon Lesbian Raven interrupting that wedding was probably for the best.
But there is also the group that grew up watching BTAS and we currently have Dick and Babs as a couple in YJ....where Dick is not operating exclusively in the Bat-verse. And Babs will be showing up in the Titans show even if it favors Dick/Kory. So I'm not seeing at all how it becomes irrelevant outside of wearing certain shipping goggles.