I bet we have a winner!
You have forgotten about the “Trimline” flavor of landline phone. E.g.:
Those wall-mount just fine. And that niche would fit that phone like a glove. The 7th image in that Amazon link shows how to do a wall-mount installation. That Amazon phone of course is a (sorta) modern device with memory, batteries, etc. But it’s the same form factor as the original 1960s Ma Bell dumb POTS phone.
Back in the day the real Bell System Trimline phones required a 110v outlet to power the backlit buttons. It would still make & receive calls and ring just fine without the wall wart, but if you wanted the backlighting, you had to have a wall wart.
Given the age of the house, this may very well have been a builder original feature that was so tres moderne at the time. Imagine the convenience of taking a call in the bathroom! Isn’t 1965 great!
Separate idea ...
I had something vaguely similar in my last condo. I bought it from the mad tinkerer who did a full remodel. So I had the benefit over the OP of seeing all his wacky innovations as he was actually using them. And I could talk to him about why (and how) he’d done what he had done. Some of his … features … were clever and versatile, but most of them were very, very single-use and were mostly a burden to me once I owned the place.
The condo had an oddly shaped master bathroom. The odd room shape wasn’t his fault; the condo had been built that way. But how he made use of the oddness was … odd in several ways.
Anyhow, he had a ~6"x6"x6" niche in the master bathroom. With a 110v outlet and a CATV connection. As he used it, there was a ~14" flat panel vid monitor / TV on a swivel wall mount that was installed into the niche. So the monitor could sit flush to the wall with all the swivel mechanism hiding inside the niche. When seated on the throne the TV was right there above and to your right at about standing eye level.
It was also off to the side of the double sink. You could pull on the edge of the monitor and it’d pivot to face your ear while you were shaving or tooth-brushing or whatever. A quick glance to your right and there was the TV. How convenient. ???
This guy lurved him some TVs. The condo was 3 bedroom, 2.5 bathroom, ~2000sf. He lived there alone after his wife had died a couple years previously. 7 televisions. The few times I visited the place while he was there, they were all on & blaring. Uggh; not my style. But to each their own.