[SpringheelJack]

But an old brick house? I could see it (maybe) if it was the home of an absolutely 'essential' figure of profound historical significance, but the Beatles' drummer?

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.

[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. 

[Luddite Patent Counsel]

Actually, Stephen Foster's home has been preserved, and is still a tourist attraction. It was moved to Greenfield Village at the Henry Ford museum in Dearborn, MI. I've been there, and it's pretty cool.