Seems to me that paying a coaching fee is the same as paying for tournaments or books.
Living with someone is different though, a lot depends on their personality. Of course my first impression is "who cares, I'll put up with Naka (or whoever) as long as he's a good coach, I could learn so much!" But I've had bad house-mates before and nothing is worth that kind of stress
As long as they're a decent human being though, then sure, they can move in for 10 years
If a 2600+ GM who's willing to coach/train you but with no cost but instead as a exchange wants to live with you without paying rent would you let them ? Or how about in exchange for his/her services he gets to pick 1-3 chess books a month that you pay for him ? Or all he wants in exchange is for you to pay his expenses for tournaments every other month ? Would you take any of these deals also if the player is famous like Hikaru Nakamura would you consider doing all 3 just be coach by him ?