There are, I would initially propose, three rough tiers why that is important.
In the immediate, the American Populace will not support an alternative - we won't put blood or treasure for it. Sine blood and treasure are required expenditures in order to defend US interests, however, the support for the exansion of our founding value set is a required prerequisite for any effort which we expect to be publicly sustainable in the face of opposition.
In the near to mid term, the Islamic world has spent the last century or so looking for a replacement to the Ottoman Empire as a governing venue that would allow them to reclaim their pride/place/self-direction/what-have-you. They tried constitutional monarchies and that didn't work, so they shifted to military-led pan-Arab socialism. That didn't work, so many shifted to Islamist Fundamentalism, which is now in the process of not working. It is in our interest to ensure that A) Islamist Fundamentalism doesn't work and B) the option the region shifts to afterwords is support for some form of liberal governance.
In the long term, increasing the portions of the globe governed by more liberal and representative structures offers greater security to the US and her interests as well as greater enablement of US policy objectives.
All three of these tiers, it should be noted, apply broadly to the Anglosphere at large and the "West" that has been influenced by it (such as, for example, Japan).
It is also the right thing to do.