When we were in Argentina last September we visited a farm which had a mobile milking shed.
The main reason for using it there is that the land is leased. The mobile shed enabled the lessee to have a dairy farm without investing capital which he wouldn’t be able to recoup when the lease ran out.
I can see possibilities for mobile sheds here for emergency use, for example during prolonged power cuts or after earthquakes; but I wasn’t sure if our environmental requirements would enable them to be used more permanently.
However, Milking on the Moove has posts on the mobile milking system; mobile cowshed and & nitrate leaching of dairy cows; and mobile milking system: alternative to sharemilking which suggest it could be done.