Isn't this already how it works?
https://en.wikipedia.org/wiki/Asse_II_mine
As far as I have been able to determine this is in fact how nuclear power is run in most of the world. Nuclear power is heavily subsidized by borrowing money from future generations. We are currently entering that future, as for example France has noticed recently. According to recent news stories their operator is 40 bn in debt and needs to make 50bn more in investments to keep plants running, meaning it has charged at least 110 bn too little for the power it sold in decades past.
One of the major downsides of nuclear power is that whenever the nuclear operator runs out of money, taxpayers absolutely have to pay, there is no option not to. From a cynical financial perspective this effectively means nuclear power has limitless credit and can sell power for fantasy pricing, way less than it actually costs.
So to the GP's point, if nuclear had to pay the actual, future costs of the energy it provides today, and it was baked in to the price per kWh it sells on the open market, we'd be better informed about the correct course of action.
So doing that only for nuclear would be an even greater distortion.
2. The topic of the discussion was about atomic energy
3. Yes
Plus no operator is paying for disposal, even if there were a magic place willing to accept the stuff.