A lot of these gentleman scientists were independently wealthy aristocrats that didn't need hand-outs. The fact that we don't to a meaningful extent have that sort of leisure class anymore is arguably a much bigger reason we need grant funded science these days.
It could be argued there a bit of a replication of the pattern in the space race between Musk and Bezos, but they're missing the sort of well education the aristocrats of yore would have had[1]. They employ a lot of people to do the actual dirty work, but that's not really a big difference from back then either.
