I’ve been trying to come up with a good reason for Luke to be in exile, and realized that it could have to do with the fact that he’s basically the rightful Emperor. Anyone who managed to kill him would be heir by way of conquest in the same way that Vader was Emperor after he killed Palpatine.

The Empire is no more.
To preserve galactic peace,
Luke Skywalker, heir to the
Imperial throne, is in hiding.

Yet under the leadership
of an ambitious warlord,
an Imperial remnant known
as the FIRST ORDER has
regrouped in the unknown
regions of space with a
weapon to return them to
power even without the
royal Skywalker’s blood.

Desperate for the return
of their greatest hero,
the New Republic forms
a covert RESISTANCE led
by General Leia Organa,
and has sent their most
daring pilot on a mission
deep into enemy space…

This could also explain (in a non-novel form) why Leia isn’t a part of the Republic, and in fact, why the Republic and the secret Resistance are different - all Skywalkers are heirs to the throne, and as such must remain in hiding.

Finally, it could make for a more compelling reason for Kylo to turn evil. Faced with the choice of remaining in hiding his entire life or leading a galactic Empire, it’s hard to blame him really.