This is the same thought that came to my head. Weather conditions would certainly cause a problem. Heat, rain, snow. How could a mechanic come to your office and do work on your car 2/3 of the year? the conditions won't permit it.
I suppose if everyone lived in San Diego, CA things would work out great though.
I suppose that the mechanic could come pick up your car at work and drive it to their garage/shelter - then drive it back (why don't auto shops do this now for a small fee?).
It could be problematic on the keys swap-over as you would still meet up. Though this just got me thinking, wouldn't having your mobiles RFID/NFC also do car entry & startup be cool! That must be in the works somewhere.
Alternatly some mechanics offer courtesy cars, so you can stay on the road while your car is being fixed.