It's definitely a thing. I believe ESTA now asks for all social media user names (not passwords, but I suppose the US government doesn't need those), and it is definitely a requirement for getting a US visa.
Remember that entry into the USA for a foreigner is entirely at the mercy of the border control officers. If they deem you "suspicious", they can refuse you access, and you don't really have any appeal.
> Either way, how can you make it a requirement to provide, what is not a requirement to have?
You simply make it a requirement to provide it if you have it. That is not the same as optional. If its optional then you aren't lying to immigration if you leave it blank. If it is not optional then you are.
Yes it is still optional. I travelled on an ESTA a few months ago , left the social media handles section blank, and they made no comment at the border. That said it is still very capricious.
Depends what you mean by requirement. Visiting/moving to USA is not a requirement. Not perjuring yourself is not a requirement if you don't mind staying in prison and/or paying fines. If, however, you do want to travel to USA and want do it without worrying about spending extended "vacation" you do need to fill the form truthfully. That includes giving a list of handles you have used on those listed social media sites (at least on DS-160).