^Basically all that, and also because production is already well versed for a few common focal lengths. The reason 50mm became the 'standard' focal length, despite a mathematical standard being more like 43mm, is simply because Leica and Zeiss both set up production for 50mm (they already had lenses around the 40mm mark, and 50mm for them was intended to be a 'secondary' standard, much like 35mm is) and it just so happened that workers, machines, and whole production line which were used to make those 50mms ended up being moved to/used by other companies, too, and it was cheaper for those companies to keep the 50mm lenses coming than to reconfigure for a more proper standard. Thus 50mm completely took over as the standard focal length.
For 100mm, it's much the same story. 100-110mm was often adapted to 35mm from medium format (where it was more like a 35-50mm equivalent, depending on the MF in question), and 100mm (or thereabouts) was the portrait length for decades. It wasn't really until the late 70s that 85mm started to pick up steam, and it wasn't until the late 80s that it equalled 100mm in popularity. As 35mm format was used more and more for magazine shoots, which required cropping, the slightly wider 85mm picked up in popularity and by the mid-90s 85mm was 'the' portrait length... but production was still set up for 100mm. It takes a long time to get factories to move on and to get designers used to prioritising new focal lengths. That's why even in the early 90s, when it was starting to look like 85mm would take over from 100mm in popularity, Canon still designed and released the 100mm f/2 before the 85mm f/1.8, and based the 85 on the 100's design. It was becoming clear 85mm would be the bigger deal, but it was cheaper and quicker for them to get 100mm sorted and out the door, first, and then use that to kickstart the 85mm afterward.
These days it's less about physical production and more about the ease of design (as mb66energy says, lenses around this length are often the easiest and best-corrected designs) as well as the designer's familiarity with the lengths. That will change as the older generation of designers retire and younger engineers come up.