The alternative to the Saudi monarchy was and is Wahhabist fundamentalism: far worse than the status quo. Did you envision a permanent U.S. military occupation?
The residual Saudi state would have been placed under new leadership. It would then have been a diminished threat due to much diminished financial and oil resources and the need to accommodate to a young populace dissatisfied with the severity of Wahhabi rule and the profound corruption of the ruling family and its multitudinous hangers on.
Although less plausible and desirable now, in the months after 9/11, such a plan would have been relatively easy to carry out on a showing of Saudi state level complicity in the terror attack on the US. An American ultimatum backed by military assets at the ready might well have sufficed, and, if military force were needed, it would have required far less effort and sacrifice than the Iraq war demanded.
Going forward, the potential for America to forcibly dismember the widely disliked Saudi state could be useful in extremis -- assuming that we have an administration that is credible. Since we are discussing a hypothetical scenario that I do not advocate, we may pass over counter-arguments based on our strategy against Iran and other considerations.