Danaerys is ALSO of Aerys and Rhaella's line she is their direct descendent as their daughter. Yes, Jon is descended from their line too since he's the son of Rhaegar, who is the son of Aerys and Rhaella. I'm just pointing this out because that can't be the reason why they HAVE to tell Jon. My vote is it's purely for some plot fluffing strife to cause tension.
IMHO I think it should be most important to Jon as it will help him validate his own identity with himself (e.g. why he was resurrected, why he should have a connection with dragons, why he seems "chosen" to lead this fight). I will be very disappointed if the D&D cheapen this to cause strife because I can't imagine Jon's character not shutting that shit right down and being like, "idfc about the Throne! The only war that matters is the the one against the dead, I already swore fealty to Danaerys, I keep my word I'm not changing taking it back now." Especially considering the epic blab he just did in front of Cersei. No one else *really* needs to know except Dany and Jon.