Oh, it being part of US 66 makes it make a lot of sense. I believe those were called "sidewalk highways". If it was anything like the similar sections of US 66 in Oklahoma, it would have had gravel shoulders on both sides. You were supposed to drive down the center of the concrete, and when traffic approached, you'd move to the right so you were half on the concrete, half on the gravel.
This was done to save money. Of course it started becoming dangerous as traffic increased.