Other than provide the safety regulations to minimize the risk the product harms you, the advertising regulations to minimize the chance you are scammed, etc, etc. Your commercial transaction occurs in a complicated environment, much of which is government funded, much of which serves to protect you (nominally, obviously you can debate the efficacy).
So, I agree with your post, but I'd like to give you some better reasons than the two you decided to lead with. Those both have pretty compelling free market alternatives, including private safety certifications (like the American Dental Association seal on toothpaste, don't be toothpaste without it! seriously.) and advertising regulations could potentially just be covered under fraud laws.
The biggest is the rule of law that allows people to actually have ownership. Without the government, your trip to the store would 1) have your car stolen while you're shopping (or you must personally defend it), 2) sharply decrease the quantity and variety of goods at your store (due to less safe infrastructure), 3) increase the price of goods at your store due to increased transportation costs, etc, etc.
I mention these reasons, not because you don't understand them (I'm sure you do), but because these are reasons that every person with a vision of correct government (short of anarchists, which are generally either very rare, or just dumb) can agree, too. In a free society, we socialize self defense because it drastically lowers the cost and efficiency of everything we do. The most free societies still leave the individual with an option of self defense, but societies that require every individual to provide for their own self defense at all times are significantly less free.
Also, there are a lot of really fantastic private libraries out there. While those things with a natural monopoly (like Fire Departments and power generation) work well as government services, non-profits are very much alive and important in the private sector. From libraries and museums to charities to churches.