I'm not saying he should get free access to the kingship forever just because he was King once. However, in all sense of RP he has a good claim.
Even if he doesn't become King, sticking around and gaining influence wouldn't be difficult. Players like playing with those they can trust and have seen work well for their realm.
The current PM of Rieleston tried to doe xactly this. Showed up and, like, a month later or somethng, with few messages to the realm, was asserting a right to kingship. That's what led to Rieleston's secession.
Honestly, if Perth tried something like that, my character would pretty much devote his remaining career to stymying it. I just find it so anathema and distasteful in BM to have a clique of players re-creating themselves to secure power.