Not every player moves, and certainly not with every trade.
Does he even live in the Boston area now? I have no idea; he never invites me over. If he does, and this is a concern, why is Betts so intent of being a free agent when Boston has already made him life-altering offers that would mean not uprooting his family? And if he does not, why would he uproot his family for a one year trade when he didn't do it for the first 5 years of his career?
To me, this is a non-issue...