Jon By Tradition Is Already King Of Westeros

When a King dies the crown almost always passed to the 1st born son. This would be Jon Snow, We know that Lyanna and Rhaegar were secretly married. Aegon and Rhaenys are both dead at this point so the Anullement doesn't matter. The main reason why the Kingsguard were at the The Tower of Joy is because they were protecting their King. So Jon Snow already has the throne he doesn't know it or hasn't realized it yet.