All escorts in the CVBG can go as fast as the carrier. The problem is the auxiliaries that refuel and resupply the escorts. They are noisy and slow.
So essentially, a carrier is strategically useless against a navy with decent subs. Its like submariners say, there are only two types of ship, submarines and targets. Still useful for pounding third-rate nations who step out of line though. Still, it would probably be better to invest in larger numbers of smaller, cheaper carriers, preferably with drones rather than manned aircraft and a really, really good sized and quality submarine force. The former can do the aforementioned pounding of third-rate nations, the latter can give you a decent shot of being able to maybe stop all your capital ships being sunk within the first week.