Essentially no.
One can even consider it a requirement for a developed country to support the "entertainment" aspects on some level. Now to be clear they way they support those industries can be very different.
Usually this is done under the assumption that those industries would fail without the government's support, so funding must continue no matter what.
Not at all true. US Football isn't going to fail without their tax incentives and subsidies. They will continue to exist and make money, and that's just an example. They get funding, on many levels for many different reasons but rarely is it because they would fail without it.
A great example is the arts during the renisonse (sorry can't get that one close enough for google)Renaissance. Look at Michelangelo’s "David". It was commissioned by the city of Venice, and became a political symbol for the city.
Want something older, the Roman Colosseum was more then just a stadium, it became a symbol of power and [Roman} civilization.
Today it's much the same. Come visit New England our football team is awesome. What is Brazil known for? FIFA Cup wins of course? Sydney, isn't that the place that has that fancy concert hall thingy (Sydney Opera House). It's also where P. Sherman lives (42 Wallaby Way).
These things create prestige and notoriety for their governments and nations. They give a way to "advertise" their country to others and a way to instill values into their culture. That is usually why they are funded on some level, not because they can't make it on their own, but because these things (arts and sports) are important to the people of the country, one way or another.
It's also worth noting that sports, the arts, the sciences etc. are a great "thing to do" as opposed to rioting and revolt. It also helps build community and an idea of "this is us" that is hard to wash away.
