There might be a slightly modified version of this question which might actually make sense: "Why we don't shoot nuclear waste into the Sun".

Surely, the cost of storing that type of waste here (on Earth) is very expensive, both from economical perspective and from risk management perspective. It could be very interesting to compare the costs of sending 1kg of nuclear waste into the sun (or out of our solar system, if that makes it cheaper) compared to storing 1kg of nuclear waste anywhere here on Earth, + adding the cost of the infrastructure that is required to actually store and preserve that waste, + adding the cost of people that are required to protect that infrastructure (a facility of some sort), etc...