it seems easy and logical to shove it into a rocket and send the rocket into the sun
Got to negotiate a path through all this space debris first . . .
There's a very speculative article on this HERE. Given the carbon footprint of a current launch I don't see this as being a very eco-friendly option until we develop different launch solutions. There is no current funding for this, and IMO the money would be better spent on tidal turbine r&d and other new (non-windmill) renewables technology.
Also - I feel there is something unsavoury about just chucking our mess off the planet . . . and who knows, it might just be returned one day with a little note: I think you dropped this
Disposal in space is a non-starter, LS - too high risk/high consequence (current risks of rocket failure during launch are in the 1 to 10% range) plus it's too expensive (launch costs just for low earth orbit are around 20 million dollars per tonne, which is an order of magnitude higher than typical costs for geological disposal). Also it would require an expensive reprocessing programme to preconcentrate the most problematic isotopes. We'll just have to wait until teleportation becomes the norm - beam it up Scotty!
