Why do you think people should be funded to do something just because they enjoy it and are good at it? Where is the money supposed to come from? Compared to football there are no paying spectators; compared to golf or tennis the market for gear and facilities - and therefore for advertising and sponsorships - is piddling. So the chance of being self-funding at any decent level is non-existent.
So state funding? Why are a few people pursuing a sport that they enjoy, but that is of almost no interest to anybody else, worthy of getting taxpayer's money that could otherwise be going on hospitals, schools, roads ...?
Don't get me wrong, I admire the effort and dedication that go into being a top level climber. I also admire the drive and ingenuity that a few people successfully apply to making a living at it. But let's face it, anybody with the necessary level of discipline and intelligence is also smart enough to realise that there's no money in it and they're doing it for love or not at all.
By the way, I am one of the few thousand people worldwide who have paid money to watch top professional climbers climb in a competition (Munich World Cup last year). I thought it was great and I would certainly do it again - about once a year. Compare and contrast the millions of people who pay considerably more to watch football live *every week*, not to mention the hundreds of millions of people who pay a bit less to watch it on TV.