Ok, so because of the happenings in KH1, we all have learned that Kairi is actually a princess (of Hollow Bastion to be exact). So...we saw that this had absolutely no significance in KH2 (or any spin-offs)...so my question is if Kairi being a princess will ever actually have any significance to the series.

If they need the princesses again, then yeah. Maybe in KH3.

Birth by Sleep and KH1 answers your question.

Maybe. But I doubt it. There may be mentions of her role, like in KH2- the password for Ansem's computer- but otherwise, maybe just some comments of how pure her heart is.

I think it just has to do with the powers of Light she possesses. She's not officially royalty.