I think they would just kill the boy calves, and keep the girls.
It takes time to breed a herd of cattle. My friend had an outbreak of foot and mouth and he lost his whole herd one time. It took years and years and years to build it back up. At best you can double your herd size every year. In practice, though, some cows don't produce a calf every year. Also, there are cows that you don't want because they don't have the traits you want. But once you have the herd size you want, it is a steady state thing.
I tried to find some place to find the volume of cattle traded that's not destined for slaughter, but the data doesn't exist. It seems that dairy cows are traded mostly via want ads on the internet these days. Here's a typical site that specializes in it: https://www.dairylivestockservices.com.au/stock-for-sale/ Notice how all of the livestock is fully grown. That's because these are livestock from failed farms. I don't think anybody sells calves because there just isn't a market for it. You can't sell calves for meat either, because as I mentioned earlier, it's not economical (the price for a meat calf going to slaughter is only $125!)
It is sad to think about it, but the reality is that milk production necessarily relies on the death of cows to stay economical. If we drank a lot less milk and were willing to pay maybe 10x the price for it, then you could change that fairly easily. However, it's just not possible at anywhere near the price point we have for food right now.
Nut milks are an odd thing. They aren't really nutritionally the same nor do they behave similarly while cooking. The taste is lacking and I highly doubt they can make cheese. And if I remember correctly, many nuts milks are also bad for the environment - much better to just eat the nuts. I don't know if this is the same for oat milks. Soy milk is simply not edible. (I don't personally drink milk, but do cook with it).
Milk is truly one of those things that has to replace all functions for it to be a viable switch. The same goes for eggs.
All this basically to say that just because there is an alternative doesn't really mean it is viable. Cotton doesn't replace wools and neither do synthetic fabrics, for example. Not to mention that at least some synthetics are made with petroleum products. I always hope they are otherwise waste products from producing fuel (like many other plastics), but I'm not sure.
I'm don't disagree with the rest of your comment, but I think the better comparison here would be to compare nut milk to what it's substituting for, which in this case is regular milk.
Eh, not really, as cows and sheep and goats still provide valuable resources. Milk and wools, for example. I'm guessing lots of other things can be taken as they die naturally - leathers and stuff from bones and pet foods and whatnot. Sure, we could eventually engineer ourselves out of needing farm animals, but it is going to take some time.
Granted, I am excited for this meat/burger to be available to the public even if you shy away from eating it. I don't eat meats outside of fish anyway and I'm always excited to get tastier edible stuff.