I don’t understand why we are not sending these off in every direction constantly. The price can’t possibly be that prohibitive considering what we can accomplish with 40 year old technology.
"Every direction" isn't what you think it is. Even if we had a voyager travelling the "opposite" direction, once outside the solar system they'd appear to be travelling at almost the same speed with respect to the orbit of the solar system around the milky way. The solar system is estimated to orbit ~200km/sec around the centre of the milky way. Even with a perfect ejection, at the estimated speed of Voyager you'd en…
The key metric is that their locations would spread by ~40km/sec. Whether that is an interesting amount of distance in an interesting amount of time is debatable, but that's the number.