EDIT: To clarify, vaccines are not sold without a prescription. At least not that I am aware of and where I life. So for me, a sale to a private party was understood as "you walk in and order it". Obviously you can do that with a prescription. That being said, doctors practices are already administering the Covid shots in the EU. Not as unbeaurocratic as the US so.
Like many people are trying to explain to you, you're just talking nonsense. You can get many vaccinations commercially without any kind of prescription in most western countries.
Many countries even have commercial chains of shops that do this - for example example here's a price list of a company in the UK.
https://www.masta-travel-health.com/Booking/Wellness
In the UK even normal supermarkets offer for example vaccination against influenza as a normal over-the-counter product routinely.
For many of the vaccines you can just go and buy them and store them yourself without any special permission or prescription. Usually you do not want to do it, simply because it is easier for the immunization clinic to take care of it.
If you're advocating for the end of mandatory doctor's prescription for all medicine that's your right, but it's rather doubtful that it would be an improvement over the current system.
The pharmacist at my local grocery store can legally prescribe me a vaccine on the spot at my request, and an assistant can administer it. The pharmacy in my local grocery store is also a private business. For all intents and purposes, yes, I walk into a pharmacy and buy a vaccine.
My doctor can give me a vaccine, but it has been a long time since I got mine there. I generally the pharmacy because they give me a discount on some sort of item I'd buy anyway.
Yes I can literally walk into a shop near me and buy an influenza vaccination at the same time as a bottle of coke from the same supermarket.
> Not without going through a doctor before hand
No prescription needed, no doctor or nurse involved.
Simple commercial transaction.