I don't see why dairy should be subsidized but some plant milks aren't exactly environmentally friendly either. The best can be said is they're better than dairy, assuming the same land could be used for both. But they can be devastating in their own right. E.g. to grow 1 almond (i.e. one kernel) takes over 3 gallons of water. Other crops used to make milk like oats have lower water consumption.
The almond example is frequently brought up, but this is still half of what dairy milk requires, without taking into account the difference in land use too
the sources of the water are vastly different though. the totals for dairy milk include the rainwater that grows the grass but otherwise is inaccessible to humans. the almonds, by contrast, are irrigated. not to mention the potable water that goes directly into the final product.
They can be, in NZ there are is a huge amount of land that has been converted to dairy through massive irrigation schemes which has caused massive problems for the rivers that flow naturally through these places... I imagine there are other places in the world used for dairy that wouldn't be suitable if not for irrigation?
The environmental problems of growing plants isn't because of the individual plants, it's because the farming practices used are bad (conventional industrial ag, synthetic fertilizers, monoculture, etc). In a well designed polycultural system, almonds can have their place too. But there is no way to make animal ag sustainable, and since that has both deep ethical and health problems as well - why bother?
Here's why dairy should be subsidized. Because all farms should be subsidized. Most of our food production needs to be subsidized to prevent bad economic shifts creating financial hardships that sink farms and lead to a food shortfall.
I mean, here's a microcosm for you. Some seafood verticals had price swings recently, and when the swings hit bottom, it was actually cheaper to keep the boat in port than go out for a trip. If the swings remained or kept going down, it would have tanked some of the smaller fishing companies. So when that swing would end, the shortage of production would have the opposite effect - dramatically higher fish prices. Yes, that'll get people back into the industry... bigger businesses that will carefully milk the increased prices instead of simply increasing food availability.
Now, the way dairy and and beef farms are subsidized is a problem right now. Even most farmers are against it. Most dairy farms don't get a penny (and in fact, PAY IN. I'm not kidding), while the larger factory farms get their feed fully paid for and large scale production subsidized.
That does mean you're probably not actually seeing a penny of price savings from the subsidies. People tend to forget that when blaming subsidies in the price of milk vs plant-milk.