Why is trash from the ISS sent down in some of the cargo vehicles. Would it not make more sense to dump it overboard in the downward + retrograde direction (as described here) and use reusable cargo craft even if the down mass is less than the trash volume?
Dumping it into orbit, even retrograde, will still leave objects in orbit, slowly falling down until they burn up. But for that entire period of time, they become possible hazards to anything in that orbit or lower.
A launcher with some minor amount of velocity would speed up the deorbiting, but it would still be there. You would probably want it somehow integrated into an airlock of the appropriate size. Using Quest (US Segment) or one of the Russia segment airlocks would probably waste too much atmosphere with each cycle to be worth it. The JAXA Kibo module has a small experiment airlock that might be better suited, but probably would want something more designed to task.
The Progress/ATV/Cygnus vehicles are there, they are empty, safer to put the trash in there, than anything else.
Ironically, I always thought that filling a Dragon up with any extra volume/mass of garbage would be an interesting business model. Sell the stuff to nutty fans like me. Would you buy space garbage? I probably would, at least once, and there are millions of nutso's like me, all around the world.
Conversely when they swapped out the Hubble solar arrays, they just 'threw' the olds ones away. They are large, so easily trackable. Visually reflective, so trackable. Being large in surface area and light (Aka: Fluffy, and NOT Gabriel Iglesias, even small atmospheric affects become magnified quickly.
Re-reading your question I see implied a secondary question, which is, why are Progress/ATV/Cygnus not recovered, like Dragon/Soyuz are?
That is because re-entry is hard and tricky. In theory Progress should be a piece of cake to make re-entry, since it is basically a modified Soyuz. Just put back the landing features on Progress. (Yes it is not that simple, but you know what I mean. Would cost upmass and so on).
But Cygnus/ATV were never designed to re-enter and land without burning up.
If you are not carrying super valuable stuff (Humans, as Soyuz does) or plan on being reused (Like Dragon has been) then it is not worth the cost/lost upmass that recovery would require.