You can take the tax credit and apply it to your taxes at EOY, or you can have advanced payment where the tax credits are paid out monthly to your insurance company to help cover your premiums. Using the latter method, she basically just gets free health care - she doesn't need to wait a full year to recoup her $370*12
I suspect that for most people making, say, less than $60,000 a year, paying cash for insurance and then expecting to be reimbursed by filing incomprehensible tax forms is not an option. This person simply can't afford it. Tax credits are useless when you are living paycheck to paycheck from two crappy jobs. She is probably eligible for Medicaid.
The ACA specifically supports paying your estimated tax credit directly to the insurance company on a month to month basis, meaning you don't need to front the cash before you get it back as a tax credit.
