It started with the Oath of the Horatii, a painting that some have even argued to be the first modern painting for that exact reason (although it's a minority opinion). It was originally a commission, but halfway through Jacques-Louis David thought screw it, I'm making this one for myself. And he was very vocal about it — that's he's making it for himself.

Let's be clear — artists have always done something for themselves, but not a gigantic piece in a new style meant to occupy a central place in the Salon. That was kinda new.

Later that would be one of the major ideological points of the Romanticists — folks, we're making art for ourselves. This had a big implication: if you're making major works for yourself, there's no immediate buyer. If you can sell it afterwards — great. If not — well, you painted it for yourself.

So it's the period around the 1820s' when you start seeing the emergence of this new purchase model, as opposed to the commission model which has ruled art since the beginning of settled life.

Patronage doesn't immediately go away though, it simply adapts — people who would still buy works from the same artists are still sort of patrons, they simply pay after the work has already been produced. But the nature of both art, which was slowly becoming art for art's sake, and the evolution of cultural landscape in general — both lead to the state where the support was becoming more remote, and purchases continued replacing commissions.

Still, I would say that patronage was very common as late as the time of Rothko and Barnett Newman — a number of collectors would buy their works regularly, often as gestures of support. This was before the inflated art market prices, so the paintings were still very cheap. Even big-time artists could rarely afford to just make art and do nothing else.

All that changed in 1973 at the infamous Scull Sale, and I would call that the true end of a patronage system. That was the first big contemporary art auction. The two things it did was it put contemporary art on the map, price-wise, and it attracted a much, much larger crowd of purchasers — before that, it was a niche market, and even people who wanted to buy contemporary stuff, didn't know where to do it — you had to actually know the artist or the collector, personally. Now it was like buying a game on Steam.

With this much larger crowd, the prices inflated due to open contesting in the auction hall (40 times what they used to be), and great visibility of said prices, the patronage model was replaced by the collector/dealer model, the latter being easier to handle from the buyers POV. After all, art got very diverse, so people tended to collect lots of pieces by various artists, as opposed to many pieces by the same one.

Which is not to say that the element of personal investment into the same artist is gone from today's model — ideally, that's exactly how the relationship between the collector and the artist is built, as in, the collector is supposed to be in this for the long run.