In most of the world, most of the time retail prices for bread are allowed to vary, and a bakery can offer a loaf of bread for 50 dollars or for 10 cents without issue.
You are right that there's lots of regulations and subsidies and taxes in the whole production chain of bread.
So if you want a more sophisticated version of my toy argument, then let's argue based on sliding scales, not binary distinctions:
There's lots of different products in different industries in different countries, and larger amounts of regulation don't seem to correlate with lower prices or better quality. If anything, it's just the opposite.
See especially black markets that are by definition at most lightly regulated and spring up every time the regulations on the formal markets go awry. (I don't want to so 'every time regulations become too much' because it's not about quantity so much as it is about sensible rules.)
There's no (binding) regulation on the price of bread and yet, people can usually afford the stuff.