Hey guys, question about the popular R L=J theory. So let's assume it's true and Jon Snow is the son of Rhaegar Targaryen and Lyanna Stark, and let's say he is revived to continue that storyline. I like it and think it's true, but I'm wondering what the significance is. Why does it matter? A couple of issues I have with it:

*With Stannis dead, it would make him the rightful king to the Iron Throne by all Westeros laws (I think?). But why would anyone care? Clearly it's not a prerequisite, as Robert took the throne by force. Several people think/thought they have a claim for whatever reason. Regardless, I doubt he'll gain any supporters as a Targ.

*Would the North still support Jon Snow if they know his heritage? I'm sure there's some bad blood between the Northerners and the Targs, seeing as how they brutally murdered the former Warden of the North and his heir, and allegedly captured, raped, and caused the death of Lyanna (in addition to the whole war thing). Being the son of Rhagegar would presumably make him more Targ than Stark, yes?

*Is there any way to prove who his parents are? I presume there isn't any kind of CSI forensics team or Jerry Springer that can test his DNA (unless there's some defining characteristic in Targ blood). Proof aside, I'm not sure who would be willing to spread that information who is also someone Westeros people would believe/trust.

*And let's assume Jon Snow figures out who his parents are. Would he care? He saw what's coming. The only way I can see him leaving the Wall is if he thinks he can gain some kind of power in Westeros and recruit more soldiers and gather more tools, but I'm not sure if him being a Targ changes anything for him.

tl;dr: Basically I'm just wondering what the likely scenario(s) is if R L=J is true and why it's significant. I guess maybe Baelish can use him? Let me know if I'm wrong on anything. Thanks for any answers!