[ineedasername]

Whether or not that would be better for society, it would very much violate constitutional freedom of speech. There is no "how about we don't allow" in this case. Or rather, the way people would have to do that is through a constitutional amendment.

It would also set a bad or ambiguous precedent. Are TV, radio, newspapers off limits too? If so, what about the annual State of the Union address to the nation? What about the (yes, small) group of people who don't/won't/can't use the internet?

It also wouldn't really help all that much: As you said, nothing stops normal citizens from posting links: similarly, nothing would stop them from posting to SM everything their favored politician writes on their official site. It might stop the specific politician from posting stuff, but that just means it would take a few extra minutes to be posted by someone else.