A few things.....

It's really hard to get things into space. We can send up an empty trash can every now and again, sometimes we can send up a half filled trashcan. To send up more just for the purpose of dumping is realistic. We aren't talking about a few dozen trashcan here, we are talking about tens of thousands of barrel of wast and waste products like spent fuel rods, radioactivity cooling water, etc.

It's cost prohibitive. I can't remember the price but per pound it's extradoinarily expensive to send stuff up. I think it's like $40,000 per pound to launch supplies just to the space station. Now extrapolate that out to some location I assume you are thinking the sun, 90 million miles isn't too hard if we get the payload going on the right trajectory I suppose.

Finnally, we would have a duty to track each and every payload making sure we know where and when they make it to their destination. If a waste package doesn't make it to the dun it will likely end up crashing into Venus or mucury, or go jetosoning off into space. It might boomerangs back to earth, last thing we'd want is radioactive flaming trash raining from the skies. We owe it to our future decendants that will likely be off exploring and mining the asteroid belt to not run into Un tracked nuclear waste.

A practical concern I have is the rocket fuel expended in the launch will become radioactive. How many of those trips would it take to poison the air and ground water with nuclear fallout from its exhaust and discarded rocket boosters?

Unfortunately the space idea at this point isn't feasible.