I'm interested in what people would continue to do if they were no longer paid for doing it. Obviously, there is a large class of not particularly enjoyable jobs which are necessary for the effective functioning of society. And there is a class of activities - like games - which are not necessary in a practical sense but which people engage in just for fun. The interesting areas are between these extremes.
Of course, a lot of people enjoy their paid work, but part of that enjoyment usually derives from the status and the money that it brings, and I suspect that, even if they could afford it, few professionals would continue to work if all the work was pro bono!
My brother is a professional actor, and he will occasionally help out with a student film, or do something he considers worthwhile on the stage for a pittance. But his identity as an actor is dependent on properly paid work.
Journalism is an interesting case. Bloggers generally blog for no financial reward and a fair percentage of the material is professional standard. Obviously, the intrinsic rewards of writing and research (if it is being read and/or utilized) are sufficient to keep these sorts of activities going.
Another interesting area is academic research in the humanities. I know a university professor who spent years (on and off) as part of a team translating Proclus (a 5th-century neo-Platonist with some pretty crazy ideas) into English, which was good for his career - but would he have done it if it did not enhance (albeit indirectly) his pay packet? I doubt it - but I may be wrong. I know of other, older scholars who will happily take their labors of love into retirement.
Despite the exceptional cases, funding matters - in the arts, in social areas and in science. Many - most? - areas of the arts and the humanities would wither away without financial support. Individual initiatives could never replace social spending by government and large private organizations*. And most areas of science depend on a combination of government and commercial support to maintain critical mass.
The hard truth is that much of the support that these activities depended on in the past can no longer be relied on.
There are humanitarian issues at stake here (I would place them above the arts and pure science in importance), and many will suffer.
However, in areas in which human suffering is not at issue, the process may be bracing to watch. A giant social experiment is in train which will determine which (intrinsically valuable) human activities will remain live options into the future.
*Spending by government on social welfare and similar programs can, of course, have adverse consequences. However, I am making the (relatively uncontroversial) assumption here that governments do have a legitimate role in providing a safety net for those in need.