Detractors to this theory argue that it is more likely that Luke will continue to tutor Rey as a Force ghost because there's no canonical evidence to suggest Leia ever received similar training, making her an unsuitable candidate to become his replacement. However, what the theory and its critics assume -- perhaps falsely -- is that Rey still needs a Jedi mentor. The curmudgeonly Skywalker was overtly reluctant to train his eager apprentice in the first place, and the pair parted on bad terms. There's also probably little more he can teach her that she can't glean from the sacred Jedi texts she salvaged anyway.
By the end of The Last Jedi, it was also clear that Rey's Jedi training was already complete -- or near enough complete. She resisted Kylo Ren's call for her to join the Dark Side, she ran rings around the First Order with Chewie in the Falcon and, most importantly, she moved some rocks around with her mind. Rey doesn't need any more Jedi Masters in her life, but what she can still learn from is Leia's lifetime of experience as a dedicated diplomat and military leader. Sure, they're skills that aren't as flashy as learning to wield a laser sword or manipulate people's minds, but Leia's resilience and sharp wits have ensured that she's outlived her greatest allies and enemies.
Having Leia as Rey's final mentor would also complete an overlooked pattern that the sequel trilogy has set up: Each of the original three human heroes from the original trilogy have taken turns imparting their specific wisdoms onto Rey. She realized her potential as a pilot with Han Solo in The Force Awakens, then tapped into her Force-using potential with Luke Skywalker in The Last Jedi and now she can hone her leadership and strategic skills with Leia Organa to destroy the First Order in Episode IX.
Not only would the completion of this cycle make Rey the most well-rounded Star Wars protagonist, but having her potentially take Leia's place in the Resistance's ranks -- in the way she's already taken Han's place in the Falcon and Luke's as the "last Jedi" -- would finally give the lonely orphan we've been following the sense of familial belonging she's been searching for.
Rey may not have any blood ties to any established family in the Star Wars canon (if the revelations from The Last Jedi still stand) but the Skywalker/Solo/Organa torches seem to have been passed to her nonetheless.