I think this is overexaggerated in the popular consciousness. Most of the famous intellectuals weren't really big aristocrats. Yes they mostly didn't come from dirt poor peasant or serf families. But they also weren't, with some exceptions, highest nobility. It was much more common that they secured funding through patronage from or got hired by the aristocrats. The aristocrats didn't really do the hard work themselves, again with some exceptions.
[1] https://en.wikipedia.org/wiki/Lunar_Society_of_Birmingham
But for example Galileo from Wikipedia:
> Three of Galileo's five siblings survived infancy. The youngest, Michelangelo (or Michelagnolo), also became a lutenist and composer who added to Galileo's financial burdens for the rest of his life.[22] Michelangelo was unable to contribute his fair share of their father's promised dowries to their brothers-in-law, who later attempted to seek legal remedies for payments due. Michelangelo also occasionally had to borrow funds from Galileo to support his musical endeavours and excursions. These financial burdens may have contributed to Galileo's early desire to develop inventions that would bring him additional income.[23]
Or Kepler:
> His grandfather, Sebald Kepler, had been Lord Mayor of the city. By the time Johannes was born, the Kepler family fortune was in decline. His father, Heinrich Kepler, earned a precarious living as a mercenary, and he left the family when Johannes was five years old. He was believed to have died in the Eighty Years' War in the Netherlands. His mother, Katharina Guldenmann, an innkeeper's daughter, was a healer and herbalist.
I think the pattern is less that they were so free from concern that they started to research, and more that they worked hard to get funded. And often incidental jobs, like calculating easter and astrology stuff (Kepler in Prague) and to the science as a bonus. Similar to how artists were mostly commissioned (like Leonardo) but also did their own "passion projects".
The typical intellectual was not some duke or baron or huge lord or the son of such. They had to be somewhat stable of course, but that's also true today. Today's professors also don't typically come from abject poverty.
Nevertheless, my general point stands in that their research was almost never their job and they needed other means to support themselves, just like artists. And this was true throughout history until the paradigm shift described in OP’s article.
Where is this coming from? Nietzsche was a university professor. He did however serve as a medical orderly in the Franco-Prussian War.
For the examples you listed, were their famous research achievements really part of their university job description?
Otherwise it’s more like Nietzsche working as an undertaker or Einstein working in the patent office just to support themselves. Naturally many such people would opt to be teachers to get by, that doesn’t necessarily mean that the university was a research institution.
Earlier many philosophers and mathematicians were also priests or monks, that’s also a lifestyle that allows for research without worrying about supporting yourself. Similarly during the scientific revolution it was mostly hobbyist aristocrats that drove it, those who had the means to support themselves while doing free research.
It’s the same story with most famous artists actually, even now. Most of open-source even operates that way, and it’s an important foundation of our modern world.
I don’t really know what to do about that, it’s not like giving everyone universal income would work either, most people do not have this impulse. And grant systems are pretty flawed too. But there is some important insight in the observation of how much has been achieved by people trying to do cool things as a hobby. It’s just really hard to support that systematically, almost by definition.