The modern dairies can get by without alfalfa. I know of farms that have been continuous corn for decades. I am thinking of going back to all corn on corn. I did it for about 5 seasons in a row. Soybeans are really hard on fertility and they take about 3x as much pesticide as corn. Corn also builds organic matter quickly.
The reason dairies do so much corn is 1) they need the tonnage that corn provides 2)they need a place to put the manure 3) They need a crop that will use up the fertility provided by manure (nitrogen) 4) corn fields close to the dairy reduce hauling silage and manure application cost. 5) Establishing and maintaining a good stand of alfalfa the last 10 year has been a COMPLETE bitch, and damn near impossible. I have seen more UGLY look alfalfa the last 5-10 years than the previous 30. 4, 6, 10 inch rains and winterkill have been very hard on alfalfa. I wouldnt want to grow the crap for as expensive as it is either. A lot less failures with corn.
The dairies likely have a manure management plan that they are following. They CAN NOT apply all they want. They are only allowed to apply a certain level of nutrients.