I'm not sure what you mean by unsolved disposal. Nuclear waste from power plants is stored in secure facilities. It takes up a manageable amount of space, is low maintanance and isn't dangerous. Furthermore, future reactors will be able to reuse it; the current reactors only use up a small fraction of the fuel. So actually, you wouldn't even want to throw it away.
Also, nuclear fuel is advantageous logistically. A typical plant needs 1 train-load of fuel a year. That's a relatively small freight, you can ship that from anywhere around the world. On the other hand, for carbon-fuel powerplants, you need a train load of fuel per day.
I'd love to see the planet off non-renewable-fuels, but a big hurdle is that, unless we figure out storage, the renewable energy sources have to be supplemented with something for when it's night and there's no wind. I don't see a better option for that something than nuclear. Of course, an alternative would be for society to switch to an energy usage scheme that doesn't presume that power is uninterruptable. However, that would require profound changes to our everyday lives, and I don't think we're quite mature enough as a species to go through with something like that at scale.