Because it's a really really bad idea, for several reasons.
1. If your rocket has a failure during launch, you're likely to spread the nuclear waste over a large land area.
2. Even though we really haven't generated that much nuclear waste, it's still many many rocket-launches-worth. That gets expensive. Much more expensive than sticking it in a hole in the side of a mountain.
3. Launching something into the sun takes a huge amount of rocket fuel. It takes a Falcon-9 with a mass of ~550Mg to get a payload of ~22.8Mg into low earth orbit with a velocity of ~8km/s. The Earth is moving around the Sun at ~30km/s, so to launch into the Sun, you need to depart from the Earth at (at distance) ~30km/s. Earth's escape velocity is ~11km/s, which means that from low earth orbit, you need to get up to ~32km/s (sqrt(30^2 + 11^2)). So your ~22.8Mg payload in low earth orbit needs to include a rocket that can add ~24km/s to its velocity. If we assume a rocket with a fairly decent engine, with an Isp of 4km/s, then we can plug that into the Tsiolkovsky rocket equation. The remaining payload that can be flung into the Sun is a grand total of 57kg. All the rest of that ~22.8Mg is rocket fuel. Per SpaceX Falcon-9 launch. This is not an effective way to get rid of nuclear waste. (Note, it may be possible to increase efficiency by making use of gravity assists from other planets, but you still need to actually get to other planets first, so a pretty hard limit on the payload-into-the-Sun is the payload-to-Mars, which is ~4Mg. Still not very much.)
Based on a Google search, we produce 10,000 tons of 'High Level' nuclear waste every year. This is far more than the total annual lift capacity of all launch providers combined.
For context, it would require 71 Saturn V launches every year just to get that tonnage up to Low Earth Orbit!
Thank you. I did consider 1st point, but I dismissed it (maybe wrongly) with higher success rate of launches in the future, crashproofing payload etc. But the 3rd did escape my mind (no pun intended)
