Assume that the funds required were taken as a tax (a cultural development tax, say), or, if the over-patron were a corporation, from the subscriptions of all users.
The allocation of funds for the exercise, being too easy to open for corruption, would instead be made democratic. That is to say, if you use or enjoy a work, you would indicate as such in a central repository, and some allocation of your input into the central fund would be routed to the creators. This is in effect similar to how Patreon works today.
On the creator's side, the benefits to this are a much more likely source of income; since the fund is state- or corporation-backed, they are much more likely to receive an amount of money if they produce enjoyable works. To raise initial funds to shoot a movie, we can imagine a Kick-starter like system, or the current model of loans and pitches to large individual investors. One definite benefit is that if people have already "spent" the money in this fund, they are much more likely to actually indicate their preferences and allocate money to artists or tool-makers that they benefit from.
There is, of course, the possibility that creators will resort to the normal populism and cookie-cutter approach to content creation that already chokes YouTube and the AAA media industry, but to be honest I don't think that's a problem that can be solved if people continue to pay attention to what they will. Given that that freedom is more important (IMO) than the integrity of art, it shall be so.
The obvious question, of course, becomes "What does the state, and ultimately the people who foot this bill, gain out of this arrangement?" Several things (the profit motive for a corporation doing this is obvious; I will cease discussing them any further); - All media entering the public domain as it's created means that software and culture becomes much more open and universal. Everyone has access to the same media and tools, and can iterate on all of them together. - Any state doing this gets a massive advantage in the culture war. In essence, they have subsidized the production and dissemination of their national values and ideals internationally. This has a tendency for positive knock-on effects in other economic areas, as well. - The death (or at least severe decline) of the advertisement industry. This seems a bit harsh, but these companies are frictional to the economy. I cannot stand ads and would love to see that propaganda machine shut down. - Creation of more niche content. For all its faults, Kickstarter has given small-to-medium sized creatives much greater chances in finding success, and especially when appealing to market segments that tend to be ignored by large content producers. This is an extension of that effect.
There are, of course, downsides. The further spread of echo chambers, the mere fact that this is an additional cost to citizens who may not even want it, the centralization of control of media creation to a state-level entity, possible privacy issues, etc. However, I see those as inescapable trends anyway, and it would be nice to get something out of it for once.