Ha Ha! I give up!
Carriers have a significant amount of fueled ships that stay with them. If you remove the need to travel long distances to fill the tender at port, this role could be carried out by much smaller ships designed to fuel individual ships and return to the carrier.
It could give a carrier group more self sufficiency.
If the ship isn't configured for deck space, add flotation pontoons for drops in the sea and pick up of the empties. There are several ways to make this work, if it made economic sense.
One more, and I’ll move on.
The ability to fuel the aircraft stationed on the carrier continuously might be justification alone.