If my friend grows tomatoes in her back yard, should I be prohibited and fined for eating one without it first being inspected?

Inspections are there because large institutions don't always take the care they should, and as a consumer I sure as hell want -somebody- to look into it. If it weren't a government institution then I'd expect some sort of company to do it, and any restaurant that hadn't gotten inspected I would avoid.

On the other hand I -don't- worry when I use Air-BnB, because it has reviews that signify quality, and because there's not much that can go wrong with sleeping on a couch.

It has little to do with the reasons for regulating food, and everything to do with the means. In order to keep me from buying soda, you have to forcibly come between the peaceful and free association of me and another person.

You're not going to convince me that I would still buy raw milk, or that pasteurized milk would be unavailable, in the absence of FDA regulation.

How would you know if you were buying raw or pasteurized milk if there were no food labelling regulations obligating people to label it accordingly?

Just like I do now. I look for milk labeled "pasteurized" and make sure it's from a trusted vendor/brand or has a trusted certification.

There's a competitive advantage to labeling food, and there's no stopping companies from labeling food in the absence of food labeling regulations. The most trusted organic certification is from a for-profit certification company, Quality Assurance International. McDonald's published nutrition information before it was required by any law. Intentionally incorrect labeling is already covered by fraud and tort law.

While not always perfectly implemented, the government acts as representatives of the buyers in that transaction.