Because a person tuning an aid for themselves is rather likely, IMO, to simply choose more amplification since they can hear better then. Which will then backfire when they lose hearing even more. I've seen braggart reports of people with strong hearing loss and aids able to hear speech from more distance than healthy people—but is that good in the long term?
Firstly, people already have to be told to not play music too loud with headphones. And secondly, when you buy an aid, the audiologist tells you that you won't be comfortable with it for some time until you get used to it—even though the aid is supposedly tuned to the exact profile of your hearing loss. People aren't good at getting used to uncomfortable things without adjusting them to their short-term liking.
On top of that, audio engineers, musicians and graphic artists know that it's difficult to do fine adjustments of audio or graphics for long because the senses become tired and ‘burned out’ after a while and you don't see or hear the same (even just five–ten minutes is enough sometimes). Novices are likely to be unfamiliar with these effects, have less stamina for them, and unable to counteract them without overcompensating.
Agreed, that last 5% of fine tuning frequency bands etc you need a professional, but if you were going to roll out $12 hearing aids to all of the low income areas of the world 1 billion people at a time, using an android app on a cell phone you could probably give a lot of people back their hearing. Volume levels could be hard-limited in software, and people who need to exceed the preset limits could be referenced to a senior technician in those 5% of cases or whatever it might be.
Being able to hear even every other word would improve quality of life of many people. Probably one in three words is the acceptable limit of "good enough" where suddenly they are worthwhile to hassle with. My grandparents now hate family gatherings because they might understand only one in five sentences spoken directly to them because of hearing problems and the quality of the hearing aids they're able to afford with their insurance.
I'm not saying it can't be automated, just pointing out that the testing process is pretty different from what you seemed to be describing. And I left out some of the steps that aren't easy to automate: checking for fit, deciding what style of hearing aid would work best, visual inspection of the ear canal.
Why is a human tester needed? I'm not seeing any reason that couldn't be automated.