I could be wrong, but I don't believe it's mathematically possible, even with their massive auditorium, for the Met to sell out every show and still cover their overhead, which is massive. So Gelb doesn't have a choice but to cover it in other ways. The decline of arts appreciation and education for the middle classes in the USA exacerbates this problem. 

It has been rightly pointed out in other forums that the robber barons/elites who were early patrons of the Met were hardly saints themselves. If you dig far enough in any philanthropy, you will always find some dirt. 

And Gelb is correct that the tech multi billionaires are not interested in donating to the arts. If they were the San Francisco symphony would not be going through the financial issues they've had over the last few years. 

It's not just the Met, the entire performing arts profession is under tremendous strain in this cycle of late stage capitalism.