I have one car that allows 5W20, 5W30 and 10W30 and no mention of 0W20 and have another car that says 0W20 only and says use 5W20 if 0W20 is not available but change back to 0W20 quickly or next time.
Assuming that 5W meets the cold temp spec. so there is no technical reason to select 0W over 5W:
One reason could be the OCI. I think the longer the recommended oci, the more chances of 0W-20 being specified since you can formulate a more inferior 5W20 (e.g. blend) but it's hard(er) to make an inferior or "cheap oil" with 0W20 which has a superior base oil. So the longer the oci, the more of "synthetic" oil requirements (i.e 0W).
price diff between 0 and 5W could have been another reason in older days but it may no longer be an issue. So if the recommended oci is shorter, there is no need for pricier 0W.
Some say 5W20 has less vii and it's better ... I rather take 0W20 with naturally higher vi than risk it with some potentially inferior 5W blend.
I've also read that some designers (old-timers?) prefer less of a pao, ester or higher group oils and prefer more of lower group (III) oils or "syn-blend" as they are more seal friendly, etc. ... This is just a wild guess and something I've read here and there on the internet. Not sure if I believe it 100%
Basically I think oci maybe the main factor. I am a thickie and like oils with less spread but in this case, if I had to use a 20, I would never use 5W20. However, I don't mind using 0W20 even though it has a larger spread.