Paving and Tree Health
If the drive has been there that long, the trees have obviously adapted to the compacted soil in those root areas. My personal opinion is that as long as you just capped the existing drive without doing and digging or expanding of the covered root area they would be ok. But I would spend a few dollars to have a professional arborist take a look at the overall health of the trees and give an opinion before doing anything. His fee will be minimal compared to the cost of removing and replacing just one mature tree that dies.