A key difference is that the press creates its own content. With platforms like YouTube, it is user generated. There is an expectation that it is a platform that allows people to publish whatever they want.

In many regards I think "common carrier" status applies. Private companies like ISP's, telcos, and parcel delivery services are not allowed to discriminate based on the content nor the individual. This is similar in spirit to "net neutrality".

The larger a platform becomes, and the more essential it is for communication and daily business, then the more important it is that it does not discriminate.

The grey area is that platforms like YouTube both are public communication platforms, but they also curate content as well. Not sure the correct answer in that case.