Milk is a perfect breeding ground for all sorts of nasty pathogens - it's a nutrient ffs. Better invest ~160€ [1] into a dedicated fridge than have half the office get the shits because someone forgot to put the milk back into the fridge over night. I've seen that happen, and if it's more serious it may actually lead to an OSHA/food safety inspection and serious fines.
And what about a second fridge makes it impossible to forget to put milk back in it?
Milk can be obtained in resealable plastic or glass bottles, which performs the same anti-contaminant task substantially more effectively, incidentally.
I think you have a wrong idea about the size of these milk fridges. These are small, separate units with just enough space to put a milk bottle into it. Via a tube, milk is directly fed from the cooled bottle inside the fridge into the coffee machine next to it without the bottle ever leaving the fridge.
These fridges are used for coffee machines where the machine dispenses the milk as well. They make sure that the machine always dispenses cold milk, instead of the milk (and its tube) being placed right next to the hot coffee machine exterior.
dedicated storage like this one [1] keeps the milk ready to use at all times, and minimizes the risk that someone in a hurry forgets to put the milk back to the fridge after making a coffee.
[1] https://www.amazon.de/milchk%C3%BChlschrank/s?k=milchk%C3%BC...