I imagine that nuclearizing the supporting logistics vessels would be very far down the budget priority list, so it's more going from short-term to full-time "last mile operations" rather than for strategic transit.
On the contrary, Operation Sea Orbit directly proved that all-nuclear battlegroups could carry out high-speed, long-range strategic transit with surprisingly little need for support from fleet logistics vessels. The importance of underway replenishment would be greatly reduced (although not completely eliminated) in a nuclear navy.
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