Even if it were actually difficult to get to the sun, there are other options that are nearly as effective.

Jupiter would be just as good of a dump or we could just launch on an extra solar trajectory. Hell, we could just put it on a large, non-equatorial orbit around the Earth and it would be effectively gone with the added benefit of being able to recover it should we find a reason to. Space is a big enough place to dump an Earth's worth of trash.

The only problems are cost and the risk of explosion during launch.