1) Nails were expensive. Timber framing does not require any nails -- it uses dowels which can be made cheaply with a drawknife.
2) Unlike @simonsarris' wood, most wood available to post and beam constructors was not particularly straight. Post and beam is very tolerant of faults in lumber.
3) With post and beam, you don't need to square all four sides of a beam. You can get away with squaring off one(the external one) plus the spots where any corner braces go. If you are hewing with a broad axe and an adze, this is a huge time saver.
4) In rural post and beam construction, the beams do not all need to be the same size. You can use whatever tree you have lying around, as long as it is big enough. This is an advantage, as you can use a local tree and save the extremely laborious trip to the sawmill
So to summarize, you can have a bunch of low-skill farmers harvesting and preparing trees for beams. Then you need a high-skill carpenter to put the mortises in and assemble the whole thing.