A nuclear power plant produces approximately 25 tons of nuclear waste per year. Sounds a lot at first, but that's like a cube with the side lengths of one meter each. In other words, a relatively small amount in terms of volume.
The storage problem has not yet been solved to the utmost satisfaction, but this is not an unsolvable problem. The castor containers of a German company for storing the burned rods are already extremely safe, only the final disposal has to be taken care of. But as I said, this is not an insoluble problem in my eyes.