It depends entirely on your distance and path/road surface. I have used an MTB, and old decrepit road bike from the early 80's and more recently - my winter road bike as my commute is now 17 mile on back roads. If you are likely to use a canal tow path or similar rough surfaces, the MTB is ideal. In a city, I would use a hybrid, and for normal road conditions, a road bike. I do not think i is a simple as - one bike for all.
Sometimes MTB, sometimes road, sometimes a folder.
Probably prefer the roadbikes, but it depends on what i'm carrying and the weather. Sometimes the folder offers a bit of flexibility if I want to go somewhere else after work but I don't use it often for commuting.
if only roads, canal paths and tarmacked paths - road bike
if quite a lot of gravelly paths and kerbs - hybrid
if you're lucky enough to have an off road commute, then mtb, but personally i wouldn't trust myself not to get too muddy so would go on the road.
In summer I ride my fixie road bike, but in winter it's my cobbled together hybrid tourer type commuter with front and rear racks, mudguards, child seat for taking littl'un to nursery en route, AirZound for correcting poor driving decisions, on one Mungo extra wide drops etc. Much slower but still quick enough and I like all the utilitarian toys on it.