So that they can seamlessly upsell you on upgrading to a new phone that you'll pay off in installments over the next couple years.
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.
We are kind of assuming a lot when a $100 a month account obviously requires a credit check.
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.
The credit checks, the carriers would tell you, are to try to protect them against people who sign up for service with a "free" phone on a 3 year commitment (phone paid for in part by 36 installments of credits) and then they stop paying the bill. Sure the phone will be blacklisted and remain SIM-locked, but could still be used on Wi-Fi and either way the carrier can't have it back and is therefore out their cost of the phone.
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.
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.