So, if they are a majority, why don't their values dominate?
1: Moderate doesn't sell eyeballs and clicks, so extremism gets the attention, which is what it wants because it will attract more of the "curious disillusioned" for potential indoctrination
2: Until unknown critical mass of perceived-threat-paranoia, there's no need to publicise / protest / soapbox one's moderate-ness because it can be relatively assumed. ie. I don't need to explain that I'm not one of those nutjobs.
If you're asking "why don't their values dominate" on a foreign policy level, well, I'm unqualified to answer that, except to say that realpolitik is far removed from most citizens' day to day lives (the conundrum semi-explored by A Few Good Men seems appropriate to mention here).
This topic being another shard of the US' soft-power armour lost.
The more it appears that the US reached and maintains it's global superpower status with force, coercion, underhanded tactics, and other abhorrent behaviors that contravene the Geneva Convention (which are handily side-stepped by conducting these behaviors in countries that don't adhere to such laws), it only works to justify extremists groups to use whatever means they consider necessary to achieve their own manifest destiny.
In that context, almost anything becomes justified - which is nightmare fuel for the moderate middle majority.