Of course you would! Or at least you would if she'd been recommended to you by a friend or had cut your hair previously. But it might be illegal! In the great state of Montana, for example, they don't let you get a cosmetologist license unless you've graduated from high school and then completed 2,000 hours worth of coursework at an approved beauty school. And lest you think that this is to protect customers rather than to protect the interests of the beauty schools, you're at risk of having your license yanked if you don't pay your student loans.
This is a good example of how bad licensing practices tend to lead to exciting new bad practices. Once the licensing system is in place, all the incentives point toward coming up with new somewhat-plausible-sounding reasons to prevent new entry into the profession. Excluding high school dropouts or people with felony convictions or (I guess) student loan defaulters fits the bill. And yet in all these cases what we really should want is to make it as easy as possible for people to learn a trade and get a job. If beauty schools are providing genuinely valuable training to people, we should expect to see demand for their product without the state forcing people to buy it.