I don't use 'social media'* and so these regulations shouldn't affect me.
That said, it is very much the principle and the precedent this would set. The laws that would be passed would require certain powers which risk encroaching into other areas and in service of other, less 'noble', goals.
We have seen time and again that such laws end up using overly broad language and contain very few safeguards and, as such, are capable of being broadened. Even if the laws, as written, are sufficiently narrow and targeted to do only what they are there for (protecting children from online bullying that may plausibly lead to suicide), the existence of such a legal and procedural framework makes it all the more easy to extend it at a later date.
Preventing youth suicide is a cause that is close to my heart (for various reasons) but still I do not support this plan.
Teen suicide has been a problem for a long time - well before 'social media' - but there is no denying that modern technologies can exacerbate the problem. Just as the Internet can make it easier to browse a store's catalogue or share photos with friends, it can make it easier for someone to be bullied, harassed and tormented.
I don't have the answers (I wish I did) but establishing such a worrisome precedent is not one of them.
* - Yes, you could call this social media of a sort, but I don't feel it's quite the same.
** - Though not so rubbish that a trip to and stay in the hospital wasn't required. Fun times.