[Stoat]

Is the birthplace of Stephen Foster still a big attraction? He was probably as close as anybody came to being the Beatles of the 19th century

Right off the top of my head, I don't know what the typical gate receipts are for the Foster Home Tour.  However, I would suggest that Foster's music has more 'lasting' value, but that's just my own personal bias I suppose.

Would it be appropriate for tax money to be spent on carefully disassembling the Foster house, brick by brick, storing it and reassembling it exactly as it was at a different location?

I'm not sure. 

[SpringheelJack]

However, I would suggest that Foster's music has more 'lasting' value, but that's just my own personal bias I suppose.

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.