To be fair to the studios, sticking with Netflix would have been suicide.
Put yourself at the mercy of someone else's distribution monopoly and you end up a powerless, penniless sharecropper - like people who develop mobile apps.
Notably absent at the time though were many of the big cable networks and movie studios.
Disney was one of the original partners of Hulu through their ownership of ABC.
Also, such channel would likely attract attention of the regulators as a clear example of a cartel.
The cable companies got to do it for so long because of the natural monopolies of shared physical infrastructure. To be fair, Netflix has been a major internet infrastructure company and there are arguments to be made about their colocation and peering agreements and the natural monopolies there that gave them an early streaming edge, even if the internet in its early days decided those sort of infrastructure agreements shouldn't create or promote monopolies. But beyond that first mover advantage and with the internet's spirit that peering and colocation are regulated fairly and not monopolistically, who would have gave Netflix the right to become the internet's TV monopoly? Would you have voted for a President who made it a campaign promise to make sure that FCC Regulators declared Netflix a legal monopoly in charge of TV streaming?
Netflix only really ever had the first mover advantage, and it is probably a good thing in the eventual long term that Netflix didn't win everything. It goes that Netflix's early model while it felt "perfectly viable" from a consumer standpoint at the time was obviously not perfectly viable in the long term as a stable situation. The situation we are in now of too many streaming services and cutthroat competition between them maybe isn't sustainable in the long term and certainly doesn't feel "viable" to us as consumers. But it certainly seems more viable and preferable than the timeline where you need to send letters to your local Congress representatives in the hopes that they might legislate Netflix price increases and put FCC pressure on Netflix to serve the content they promised to serve.
And even then, Netflix was burning billions of dollars of cash every year to keep operating.