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The Saudi government doesn't want to fund extremism as such, it's just that their governance and control over these schools and other Islamic charities they fund is minimal and incompetent.That's a very charitable view, especially for a monarchy that exerts tight control over many aspects of life in their country. That is not insisting on simplicity. Pakistan's government, and their security services, for example, are manifestly capable of working multiple conflicting agendas. But that doesn't mean they can be excused.
As others on this discussion have pointed out, Saudi has exported both terrorism and the fundamentalism that gives the terrorist fishes a much larger sea to swim in. The US, in part because if its own problems with religious fundamentalism, is unable to forthrightly work against religious fundamentalism and other excesses in religiosity, such as suppression of women's rights, in the Moslem world when that might be the most effective way to reduce terrorist incidents. Imagine trying to end the Soviet Empire without detente.
So, yes, that is a real mess.