> equidistant from the edge of the observable universe in all directions

That seems like an example of "streetlight effect." The streetlight effect, or the drunkard's search principle, is a type of observational bias that occurs when people only search for something where it is easiest to look.

https://en.wikipedia.org/wiki/Streetlight_effect

It's not. Rather it's that every observer in the universe is at the center of their own light cone.

The fact that we can not observe anything outside our light cone is well understood.

Some of that is a semantic thing about how one defines "distant", but this is not really required by GR. In fact the insight behind the emerging "timescape" theories is that the universe isn't flat or homogenous on large scales and that different regions have expanded at different rates. Their "edges" are equally old, but may not be not equally "distant".