"traditional mainstream" is correct and usable in written English.
Example: The traditional mainstream view of the issue has shifted in recent years.
Here the machinery of traditional, mainstream storytelling threshes efficiently.
Traditional mainstream reporting doesn't want to cover something until it's meaningful to the world.
Same-sex marriage opponents often cast themselves as the defenders of traditional, mainstream American values.
To do that it will need to win over people who prefer the traditional, mainstream right.
What is undeniably happening, however, is that the continent's traditional mainstream parties are in full retreat.
This should tell us what to do with traditional, mainstream banks.
"I think a lot of people here, who are traditional mainstream Conservative voters, don't want a hard Brexit," Clegg said.
Note that the only name on the list whose image channels traditional, mainstream femininity is that of Caitlyn Jenner.
"If you're going to communicate with the broad public, it is no longer sufficient to simply do it through traditional mainstream media".
Part of her promise lies in her potential to address both a traditional mainstream country audience and also younger, more eclectic listeners.
Her generic tributes to "peace through strength," freedom and free trade were squarely in the comfort zone of the party's traditional mainstream.
