I don't think your comparison is valid. This is about privacy of communication, so it is very related. Like the department of education may come up with extra saftey requirements for school buses.
This is more about the Republican party being obsessed with undoing any rule that was enacted/proposed in the Obama era.
Food and Drug Admin (FDA) in fact is a perfect example. It can issue regulation about manufacturing facilities making food or drug. Imagine for a moment these two made-up regulations were to be issued today:
1 "any rodents discovery must be reported within X days"
This would be a perfectly valid regulation as rodents would affect your food.
2. "95% of the parking must be Handicap accessible"
This would be an overreach. Handicap parking is a matter for regulation by Congressional act (Americans with Disabilities Act (ADA) in 2010). Authority was designated to 5 agencies (ODEP, EEOC, DOT, FCC, and the DOJ). If FDA wants a Handicap parking rule, it should refer the matter to one of those five. DOT (Department of Transportation) is likely the one that should deal with parking.
I am sure with some imagination, you can make up a rule that the DoED can issue (pollution affects student performance) which will step on the toes of EPA.
* * *
So, Congress' action yesterday shows FCC can issue regulations about communication. Consumer protection (Privacy) is already designated to be under FTC. FCC Should forward the matter to FTC. And they made their intentions very clear in some interviews by news agencies.
Trump did made some statement about stream-lining the Federal Government and overlapping regulations. He made the statement in regard to EPA issuing regulations governed by other agencies. So contrary to my earlier statement, this may indeed be more than just Congress.
Whether it is pro or anti Trump. It make sense that if the authority is already designated to agency-A, agency-B should refer the matter to agency-A.