Like I said at the start, I suspect you will need a real PC if you really want to do what is normally the job of the audiologist.
I have seen the whole process done, and to do it properly you need a soundproof chamber, calibrated volumes, special software on the computer to generate the various test sounds, and a button for the user to press when they hear a sound. The data is then processed to create a profile of hearing capability, by frequency and volume. That profile is then converted into the base programming for the hearing aids. The additional custom profiles such as music/outdoors/voice/theatre and so on are simply tweaks on top of the base profile.
It simply isn't possible to create an accurate base profile without that sort of setup. I can't understand about an audiologist whispering nowadays. It needs a proper scientific approach to allow modern hearing aids to work to their full capability.
The ones I saw being programmed recently were the latest high-end Signia ones, with rechargeable batteries, portable lithium battery pack that can recharge them without needing mains power, bluetooth, universal streaming device, and apps for iOS and Android. I thought them quite expensive, over £3000 which is about $4000. (P.S. This was the discounted price at Specsavers - the list price was a lot more.)
By the way the NHS here does provide free hearing aids for all, but they are very basic low spec ones, nothing like those Signia ones.
As Jim notes, the idea is to make minor modifications to the EQ curve. My aids store three "maps" or "curves". I had the audiologist leave one at the baseline (which was the least desirable when auditioned in his office) for the sole purpose of tweaking.I'm not going into this naively. I've been wearing hearing aids nearly forty years and have had many audiograms done over the years, including one a couple of months ago. I would only be making slight tweaks to what the audiologist has already programmed.
However, considering that I would have to buy a PC dedicated to just this task I will probably not be doing it. As my beginning statement said, I am considering it. I do get frustrated with the tweaks the audiologist makes which I can't really test until I leave his office. On my temporary trial in December the last adjustment he made left me with unacceptable audio feedback which didn't show up until after I got home, requiring another appointment and visit a week later.
These Phonak Marvels will cost around $6k.