Yes, they still exist! In my limited experience the milk does taste better but I think it's because of management, not genetics.
The "get big or get out" Holsteins of conventional dairying will produce themselves to death. That is, they'll make milk even at the expense of their own bodies. To handle that, they need to be fed very intensive grain-based diets (corn and soy). Otherwise they'd waste away.
One of the local dairies has better milk, and anything derived from milk, than the others. Their secret is that some of the herd is of Guernsey and Jersey breed. Milk from only those cows is yellowish in hue, and certainly richer in fat, some would say it tastes better but it definitely tastes different. I prefer the combined milk from the dairy in question (in the US) to pure Guernsey, which is also available, depending on locale.
I would say that the effect of breeding for quantity is less extreme for dairy than for chicken meat, but it's there. The main impact on flavor isn't actually higher production by the cows, it's large-scale homogenization and high-temperature pasteurization as side effects of scale. The larger processing machines oxidize the milk more, and longer pasteurization increases shelf life but it does reduce the taste/quality further. I'm not talking about UHT, which produces a quite noticeable difference in the milk, one which some people like, just processing which leans more in that direction.
Raw milk is milk that has not undergone pasteurization or homogenization. Depending on the state (in the US), raw milk may be illegal to sell, but there are ways to work around that for the determined.
Creamline milk is milk that was pasteurized, but not homogenized, so the cream floats to the top. It doesn't store well long-term in grocery stores, but can often be found at farm-to-table stores and other specialty boutiques.
Note that the U.S. (including my parents growing up before we got milk cows) has an obsession with "reduced fat" milk. Switching from 2% milk to whole milk makes a world of difference for taste, even without going cream line.
My favorite milk was raw from our Jerseys (they have average ~5% fat compared to national average of 4% [1]), but I've had raw Jersey milk, mixed-breed creamline milk and store-bought whole milk depending on what's available, and they all taste better than 2%.
Raw milk isn’t inherently more flavorful than pasteurized. It’s by necessity consumed sooner which enhances the flavor profile vs milk that’s spent weeks going through the typical logistics chain before you buy it. But, the safety concerns are significant and you could also get pasteurized milk that isn’t particularly old.
I've been drinking raw milk almost exclusively for about 5 years (and milking my own cows for the last 1.5 years). Whenever I get store-bought milk, I'm hit by the "cooked" flavor of it. I assume it's the pasteurization that makes the difference because I've also scalded milk on the stove -- same taste.
You’re likely noticing several other factors. Scalded milk is much larger impact via higher temperature for far longer.
The real test is to blind taste milk immediately before and after pasteurization and I couldn’t tell the difference with High-temperature short-time which only hits 71.5C for 15 seconds.
At home you can try a blind taste test after heating to 60C for 20 minutes, but we use HTST because it’s basically undetectable. UHT has a longer shelf life, but there’s just a hint of a taste difference.
The "get big or get out" Holsteins of conventional dairying will produce themselves to death. That is, they'll make milk even at the expense of their own bodies. To handle that, they need to be fed very intensive grain-based diets (corn and soy). Otherwise they'd waste away.
But low-input cows can produce milk on grass-based diets without wasting away. Grass milk is healthier (https://extension.umn.edu/pasture-based-dairy/grass-fed-cows...) and in my experience, tastier, too!