@You_Fool

The problem is that you're locked into one of two inefficiencies.  By funding art, you either:
A: Fund everyone, which means you'll be subsidizing people who won't be recognized as the greatest artists of all time... you'll essentially be funding mediocrity, or
B: Attempt to only fund so-called great artists.  That's frankly impossible because, as you mentioned, it's nearly impossible for us to determine who, at this time, would be considered a great artist in the future.

In addition, one other problem: You're comparing 1800's scenarios to today.

The modern, post-industrial economy has a much higher base average discretionary income level than in the 1800's (in the midsts of the Industrial Revolution).  We also have more rich people overall.  Those are the people that buy art.  Long story short, the modern economy has more people with both the interest and the incomes to be consumers of art... preventing the starving artist scenario for people who are both talented and able to market their products.

Oh, right, and we have the internet, which means an artist can connect with millions of people at dirt cheap prices to sell their artwork.  They don't necessarily need to invite people to their gallery in their older brother's basement, except when a serious buyer is interested in inspecting the product.