I don't necessarily dislike the idea of "keep up" legal standards for speech on large social networks. I think executing it would be tricky though.

I have a few worries here:

1) There is a fair bit of supreme court precedent against compelled speech. Prohibitions on compelled speech are very important for protecting someone's right to free expression. Undermining that would be troublesome.

2) Some proposals (and the Texas law) are not content neutral. They discriminate against some forms of content. Off the top of my head, there is a vague clause which could be used by bad faith actors to target sexual expression. This is not in line with the First Amendment. That is worrying.

3) While this is probably less of a problem with a U.S. based proposal, internationally, you might have one country tell a company to take something down, and another tell them to keep it up.

4) State power.