Even if we ignore the ponies and rainbows of wormhole travel, if you want to travel to a plain black hole to use the magic teleporter, the nearest two are V616 Mon at 11 solar masses and 3000 LY away, and Cyg X1 at 15 SM and 6000 LY. If you buy into the article's assertion that you won't get burned or spaghettified on your way to becoming a nucleon paste, and you want a heavier BH, the nearest is Sag A* at 4.1e6 SM and 25000 LY away.
Anyway, to travel between the teleporter and Earth, we're talking most of the resources of a planet to accelerate a mass to substantial fractions of c. Then you've got thousands of years of collisions, radiation, and maybe (assumption?) cultural and biological challenges of living in space for aeons, plus needing another planet's worth of resources to slow down at the destination. All this makes it hard enough even to get a dozen LY to our nearest start system.
My opinion is we're in something of a Well World universe, where everyone is pretty well travel-isolated from their neighbors.