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.
This sheds some light on it to me. I guess what partly surprises me is that people seem to care more about reputation than just a means for improving the signal to noise ratio in papers or as a estimate on what will give you your biggest bang for your buck.
The other issue I see come up is the idea that if there is no signal to noise filter, then a scientist might "waste their time," either reading the paper or trying to replicate. But to me, it sounds a little bit like trying to avoid actually doing science. And peer reviewed papers don't imply excellent quality either. You should evaluate papers on their merits. It is your job, as a scientist, to evaluate the most productive approaches based on the merits of the science being done, not based on reputation.
During the 'golden age' of science, the time of the Royal Society the fields weren't specialized at all and the publication mechanism was scientists sending each other interesting stuff by post. At that time there was no meta analysis at all and there was so much low hanging fruit that the 'gentleman scientist' could make big breakthroughs in their home laboratories. But as that low hanging fruit decreased the educational paths required before being able to do meaningful science became longer and longer, then specialization set in and the costs of doing science went up. That's how we arrived at grants used to fund science.