"advocated that" is correct and usable in written English.
It is used when you are expressing opinion or advice about something. For example, "The professor advocated that we consider alternative solutions."
Ariel Sharon, Israel's prime minister, has advocated that step.
Gastroenterology specialty societies have advocated that providers routinely assess their performance on colonoscopy quality measures.
Mr. Rumsfeld's newly nominated deputy, Paul D. Wolfowitz, has publicly advocated that policy.
During his campaign, Trump advocated that Americans be allowed to re-import pharmaceuticals from other countries.
advocated that proposal on a Sunday chat show.
WLF advocated that outcome in an amicus brief filed in the case.
Other MPs have advocated that measures be pushed even further.
As mentioned, not even Mindszenty advocated that approach.
I have never advocated that.
And I have never advocated that," the Florida senator responded.
We have advocated that rehabilitation count as a work activity.
