Why do we take fuel out when there’s still energy in it?
What does “spent” mean here?
Used fuel still contains uranium and newly formed plutonium that could be recovered for new fuel. “Spent” means it has reached the end of its useful service in that reactor.
What changes while the fuel is working?
Fission changes the fuel’s composition. Some of the products absorb neutrons that could otherwise sustain the chain reaction. The remaining inventory of useful material is therefore only part of the question: can this assembly continue to support the operation required of it?
Recovering material and making new fuel is a different industrial process from leaving an existing assembly in the core. Reprocessing also brings costs, waste streams, and safeguards questions. Its value depends on the fuel cycle being considered.
Why does the fuel still need cooling?
Radioactive products continue to decay after shutdown. They release heat, so removed fuel still needs cooling and shielding. This is a separate issue from whether the fuel can sustain the desired chain reaction.
Cooling fuel after shutdown
Water pool
Dry storage
Water removes heat and provides shielding in a pool. After enough initial cooling, fuel can move to a shielded dry cask, where air carries heat away.
Are those all the same kind of limit?
There are at least three questions here: what material remains, what can work in the existing reactor, and what could be recovered for a different fuel cycle.
Still to understand
What changes first in a specific reactor: the neutron balance, the permitted operating conditions, or the economics? Answering that needs a specified reactor and fuel history.