I don't think that you and I are talking about the same things when we say "unprocessed cheese" or "non-shitty bread". Wal-mart has, in the scheme of cheese and bread available on earth, an absolutely abysmal selection - this remains so even when compared against the US more widely.
Part of this is Wal-mart's focus on a very limited number of suppliers that have many different brands/logos.
Even the mozzarella balls in brine sold in the "fancy" grocery stores are full of adulterants and other things you'd never find in quality cheese. The "fresh" bread from the bakery is lower in preservatives than the bagged stuff, but is nowhere near "good". The worst bakery in any major city in Europe has bread an order of magnitude better than any chain grocery store's "fresh bread" bakery section. (That's not nationalism: you can pick any of a dozen countries to compare.)
...and in many places in the US, that's the only/best available within a 20-30 minute drive. Food deserts (another growing problem) are even worse.
US grocery stores are very bright and shiny and have many different brands available, but the hidden structure is that almost all of those widely available come from a vanishingly small number of conglomerated suppliers, oftentimes using processes or ingredients that are banned in other countries on safety and health concerns. Even the "quality" (aka fancily packaged, more expensive) stuff comes from the same conglomerates and suffers the same problems.
My local grocery store has hundreds of small local brands that are absolutely not a front for some conglomerate. There isn't some secret that only European bakers and cheesemakers know; American bakers can and do bake the same breads and American cheesemakers make the same cheeses, etc.
[1] https://sci-hub.do/10.1111/obr.13126 Figure 1.
> From there you can add chicken and fresh herbs.
Due to the car-centric nature of the US, where it is really common to be over 2km from a market, and a trip to the market requires a) driving there, b) parking, c) driving back, the average USian visits the supermarket less frequently than people in other countries because it's more time and resource intensive. This results in larger trips (shopping carts occur in 100% of markets, and also Costco is a thing) and more processed foods with preservatives due to increased time between trips requiring longer shelf life.
Fresh herbs, unprocessed cheese, non-shitty bread, et c - these are way more common in societies that visit the store every 48h (or sometimes even every 24h if there's a bakery on the corner of your block that you pass on foot every day) as opposed to the USA where you might only go to the market every 5-14 days.
Just one more way in which the religion- and racism-motivated US shift to single family detached homes and suburbs cratered the population density and took neighborhoods, sidewalks/walking, camaraderie, local exploration, and fresh groceries along with it as collateral damage.