Sure, except that for the most part conservatives seem to be happy to watch their rights slide right down a hill when conservatives are in charge. See the entirety of US politics at this point.

Society already puts limits on children's access to media, their access to addictive substances, advertising that's allowed to be shown to them, etc. The internet, and especially social media, is a gap in the existing limits. This isn't a slippery slope, it's adding a missing set of compliance.

Social media is: media, addictive, shows unregulated advertising to them, is psychologically harmful, and their algorithms have been radicalizing them.

Regulation is absolutely needed here. I'd rather see tight regulation, rather than being blocked completely, but social media companies have been highly resistant to that. For example, they shouldn't be allowed to show advertising, they shouldn't be able to do tracking, they shouldn't be allowed to have an algorithm led feed, notifications should be mostly off by default (and any notification that is shown to primarily exist to make you open the app should be disallowed).

The problem with changes like that is that they destroy the network's engagement and remove their profit, and for the most part, it's changes adults would like to see as well. Making those changes for some countries laws would push other countries to introduce similar laws and not limit them to children.