Why nuclear-powered escorts accompanied carrier sprints

Were nuclear-powered escorts too few to support high-speed carrier movements?

The rare sprint scenario required about one nuclear escort per carrier, with another racing out from the destination group to meet the incoming force.

The Cold War requirement did not demand nuclear propulsion for every ship in a carrier group. One fast escort alongside each carrier was enough for the rare emergency in which the carrier had to leave conventionally powered companions behind and move at sustained high speed. The nuclear escort from the destination group could steam toward the incoming carrier, giving it two fast escorts near the critical area while the rest of both formations followed. A small pool of nuclear escorts could therefore support these exceptional movements.