The house in which we lived when I was between two and five years old was brand new (built c. 1958) and had an electric wall heater in each of two bathrooms, so I know they were made at least through mid-century.
When I was five, we moved to an older (1930s) home in a fancier neighborhood. It had a "jack and jill" bathroom to serve the two kids' bedrooms. This bathroom had two doors, one leading to each of the bedrooms, which took up a lot of wall space. Basically, the bathtub with shower enclosure occupied one wall, the door to my sister's room and the toilet occupied the next wall, the vanity/sink occupied the wall opposite the bath, and then there was the wall with the door to my room. Basically, there was no room to place a wall heater. My parents remodelled the bathroom a few years after we moved in, updating the bathtub and vanity/sink (changed bathtub to a newer one with glass shower doors and up to date Kohler fixtures), but there was no wall heater and probably no room for one.
Our neighbors around the corner had a large but poorly heated 1930s mansion. It used to get cold in the bathrooms, and I remember there was a wall heater (electric) in the kids' bathroom; this bathroom was original 1930s, never remodeled. I'm not sure if a wall heater was standard issue for the 1930s, or whether it was high-end and only seen in more ornate homes from that era. I used to switch on the heater in my neighbor's bathroom because it reminded me of the heater we'd had in our former (brand new) home. I wonder how many watts those things sucked up?