I would think a private company could remove the core for 25% of the government cost. Then tow it out to see and use to for torpedo practice.
I qualified on A1W for my nuclear submarine duty which was the prototype reactor that was located in the Idaho desert for the Tunaprise (the nickname at prototype for the ship).
At the prototype they had two reactors with one control room. On the ship, they had EIGHT reactors.
Why so many? It was because the reactors were closer to submarine reactors (lower power) than they were to later generations of aircraft carrier reactors.
They typically remove the core (nuclear fuel) decades earlier and then let some of the shorter life isotopes decay in the piping and the rx vessel before they start disassembly.
I watched an old test reactor similar to these decommissioned in South Carolina. Even after decades, it was quite a job.