A destroyer can refuel at sea, but the transfer takes time and exposes both ships to risk. The ships cannot manoeuvre as freely during replenishment, which becomes a greater problem near an enemy. A destroyer occupied with taking fuel is also unavailable for its normal screening duties. Greater endurance gives the fleet more freedom to manoeuvre before it needs another replenishment. Otherwise the destroyers can hold back the capital ships they are meant to protect.
Notable Point · 4:15-6:51
Why destroyer endurance matters to the fleet screen
Refuelling interrupts screening, restricts manoeuvre and can force a fleet to accommodate its shortest-ranged escorts.