I could see payroll providers offering it as an option, similar to sending money to retirement plans, post-tax insurance, charitable contributions, etc. I have seen payroll plans that purchase goods either up front or on layaway.
This is how it works by default in New Zealand, and it works quite well in my opinion.
If you have a student loan then your tax code changes and student loan repayments are deducted from your pay like payroll taxes, at a rate 12% of every dollar you earn over the repayment threshold (~$20k NZD annually). In effect (combined with Kiwisaver, our retirement savings plan deducted at the same time) this means that you don't really need to think about your student loan when earning wages or a salary as your take home pay already accounts for this.
You can add manual repayments, but this is seldom done in NZ as student loans are interest free under certain conditions so there is less incentive to repay them quickly.
That's really interesting perspective, I had no idea that's how it worked in NZ. I suppose it works seamlessly in NZ as the loans are originated by the the NZ government. Could be interesting if student loan services in the US offered a BPS discount if the payment auto deducted from a paycheck.