Somebody’s going to come along and say it, so I might as well be first: it depends on your definition of science.
Mathematicians can still go off by themselves and come up with great results. Andrew Wiles did it with Fermat’s Theorem.
And Stephen Wolfram made a fortune from his Mathematica software and went into a closet and came out with nothing less than A New Kind of Science.
Theoretical physicists can do more or less the same thing, but already we’re at a crossroads. No one theoretician has made a huge breakthrough as an individual since Alan Guth reinvented inflation. The various theories competing for theories of everything are the result of dozens of individuals taking one another’s work and refining it, testing it, expanding it, and elucidating it.
And more importantly, physics can’t truly advance without the experimenters confirming (or rejecting) the predicted theoretical results. And experimental physics is seldom anything that can be done outside a well-funded laboratory, even when supercolliders are factored out.
The same kind of split is more or less true in other disciplines, although to a lesser extent. There are theoretical biologists - try reading a paper on, say, population genetics - but most, like Darwin, spend much of their time in the field, and need the backing of a major institution to afford fieldwork. Or the government, which is what Darwin did.
Darwin, of course, wasn’t truly rich: he received an offer to work as a naturalist on the Beagle, but it was an unpaid governmental position. His father had to put up the money to support him and pay his expenses, 30 pounds a year IIRC. A goodly sum of money in those days, but not real wealth.
In short, if that’s still possible, it’s yes and no. Yes, science is more expensive, but no, then as now other people put up the money. No, science is collaboratory because there is so frigging much more of it to comprehend, but yes, individuals, now as then, can still do major individual theoretical work.