seems to me a political explanation is more likely, probably related to the holy war with Iran. In that case I never really understood why we took an anti-theocratic stance there.
Iran provides the perfect example of why we tolerate Saudi Arabia. From 1901 to 1951, Iran's oil was controlled primarily by the British. In 1951, a democratic movement lead to the nationalization of the oil industry, which quickly led to a CIA backed coup. For the next ~30 years, a Western backed dictatorship ruled and their violent rule lead to the 1979 revolution being overtly hostile to the West.
The West fears any other Saudi government would end up hostile to the West, given their decades of support for the monarchy.
If you hold an election after toppling a non-democratic government, you never know if that's going to be the last election or not. Also, you just can't trust that the people will elect your "guy". If you're already "controlling" the current leadership, no need to turn over the apple cart.
Very unlikely. Any military involvement anywhere near Mecca and Medina is off the table barring being invited or some utterly insane scenario.
Sometimes its useful to think inside the box
But yeah current Saudi Arabia is a good deal for the US, hard to get others so heavily intertwined financially. Might as well not touch it.