I have the exact same problem, I was about to make a post about this but I have just seen this one. Its actually very annoying that it occurs I want to populate a entire region but I havnt got the motivation if its going to look so silly. My region is all medium tiles aswell but I notice it happens on ready made regions too so its not to do with that. I too noticed that its in a checkerboard pattern. I do not really see a reason why the game would be made to do it on purpose.
I remember seeing a Download that allowed Sims to work from their houses. At the time I didn't really think I would need it but I now have a problem with the No Jobs zots and abandonment. Rather then build a realistic city with appropriate commute times I would prefer it if I could just let my Sims work from home. I am 100% sure this exists except I didnt read much about it so im not actually sure if this would solve my problem but its worth a shot. If anyone can find this I would be very grateful. -Stephen.