In theory, on paper, there's no reason you couldn't do it that way. In practice, the administration of that technical system is non-trivial and requires access to those companies' infrastructures, which they are not likely to want to provide.
I think it's certainly something that should be on the table for discussion about a long-term solution, but in the short term, if what we need, for example, between now and October 2019 is the ability to remove intentional hate speech and illegal content off the Internet in a hurry, we're going to have to find a more straightforward mechanism.