I don't know. Foster mostly survives on a few songs, as I suspect the Beatles will. Things like "Michelle" and "Yesterday" will probably stay sung for as long as "Oh Susanna" and "Camptown Races" have. But things like A&E putting the Beatles on a list of the "100 Most Important People of the Last Millenium" will die a deserved death with the Baby Boomers.
Regardless of the relative merits of their music, I still think that I would be aghast at the notion of taking a house apart, brick by brick, storing it, and then reassembling it at another location merely because of the fame of the person who once lived there. If the house was particularly beautiful and grand or represented an important architectural style then that might sway my opinion, but in looking at the Starr house, I see nothing remarkable about it whatsoever.