Interview-based studies of foreign fighter motivation yield little or no evidence to suggest that breaking US support for the home country government is a significant motivation. The motivation cited is consistently of the "expel the infidel from the land of the faithful" variety. It's also hard to ignore the reality that foreign fighters have been effectively recruited from countries where the government was not supported by the US, such as Syria and pre-revolution Libya, and the foreign fighters have been successfully recruited from all of these countries to fight in wars that had nothing to do with the home country government, such as the resistance to Soviet-era Afghanistan.

This theory seems to me to be unsupported by any evidence, and it's a dangerous theory: it suggests that al we have to do to de-motivate foreign fighters and terrorists is to fix the governments of Saudi Arabia et al. This we cannot do, and trying would make a huge mess and likely give us a great deal more terrorism.

US military intervention in Muslim countries motivates foreign fighters and provides them with a target. Easiest way to manage that is less intervention, and certainly less occupation, which provides enduring motivation and static targets.

We deceive ourselves if we pretend that these problems were created by meddling and that they can be resolved by good meddling. The answer to bad meddling isn't good meddling, it's less meddling.