Why would a phone company know a person's SSN?!
As Brit-expat+US-resident (since 2012) T-Mobile got my SSN when I signed-up for my pre-paid first mobile phone plan in 2012. Paying $50/mo was quite a shock when equivalent (or rather: far superior) service was available in the UK on a PAYG (not even pre-paid!) basis for £10/mo.
...and now I'm on a $110/mo postpaid plan because eventually you get tired of the limitations and just grin-and-bear-it.
Also, many postpaid plans (like my home ISP) require SSN because they are providing you service on credit. Postpaid cell paone plans have been the "default" in the US for a long time, though prepaid seems to be gaining market share.
They require a SSN because people don't care and it makes it cheaper to offer the accounts, not because it would actually be a big problem to sell internet service without credit checks.
Now, as for why they still do the same credit checks when you bring your own phone, I suspect "Because F you, that's why" is the gist of it.