Carrier based tankers will be dependent on underway replenishment for the supply of the said fuel, and they will be insanely expensive to run. You will need a whole carrier battle group with it's escort and stuff to replace about 1-2 KC-10s (depending on the mission radius [1] - and yeah, the top mission radius of this thing will be abysmal, not even 1/3 of KC-10 and at best half of KC-135).

This is just to increase the range of carrier based aircraft. Avoid putting carriers too much in the harm's way.

[1] https://fas.org/nuke/guide/usa/bomber/kc_comp.gif