The reason we get long term nuclear waste is that we put uranium 238 in the reactors. It’s not a fuel, it’s an impurity. Uranium 235 is the fuel. The uranium used in civilian power reactors is only a few percent fuel, and over 95% U238, nearly all of which ends up as nuclear waste. This is called ‘burn-up’. Civilian power reactors achieve very low burn-up, less than a few percent, and the rest is long term waste.
The reason for this is political; the uranium 235 is never purified because countries don’t trust each other not to make bombs.
There are reactors that can cook down the “waste” or “spent fuel”, at least a bit and maybe lots, but development has been minimal. That was sort of the plan originally. Some of the U238 turns into plutonium, which is another fuel. It can be reprocessed out of the spent fuel, but then you need a different type of reactor to use it. But these reactors are even more expensive and complicated so none were built so a stockpile of plutonium built up which had to be guarded all the time; the UK built up about 60 tonnes I think before they thought they’d better stop making it.