I don't think that they actually do in practice. Last time I opened an account with Comcast they required your social security number. Same with an AT&T cell plan.
As many as 1 in 7 SSNs may have been accidentally used by more than one person. [1]
Unlike Australia's TFN or the UK's VAT, SSN has no self-check, making it rather easy to just... Generate one that works.
And all an API check of the number will tell you, is what an attacker would already have: DOB and Place of Birth.
[0] https://pnas.org/doi/full/10.1073/pnas.0904891106
[1] https://www.nbcnews.com/technolog/odds-someone-else-has-your...
Strictly speaking they require /a/ Social Security Number, not necessarily /your/ SSN.
When I signed up for my most recent cellular service, I hesitated at giving my information to the guy in the store. I told him that since it was a pre-paid account I wasn't asking for credit, so there's no need for him to have my information.
He was OK with that, and pulled out an ID card the store keeps in a drawer for just such occasions.
Salespeople have a sales quota, not an enforce-the-rules quota.