A couple of points:
1. Escort carriers were actually much SLOWER than fleet carriers. They were built primarily from converted transport hulls. There was a separate category of carriers that were fast enough to keep up with the main fleet carriers but were smaller. Those were called “Light Fleet Carriers” (CVL’s) rather than “Escort Carriers” (CVE’s). CVL’s were typically converted from cruiser hulls (The Independence class CVL’s were conversions from Cleveland class cruiser hulls.) The primary mission of Escort carriers was ASW, which is why they didn’t need much speed, and since you can never have enough convoy escorts, they wanted their CVE’s to be as cheap as possible… It is for much the same reason that the Destroyer Escorts (DE’s) were a little slower than top-of-the-line fleet destoyers: they needed to be faster than a slow convoy or a sub, but not fast enough to keep up with a fast carrier attack force.
2. Actually, BC’s would make more sense as fleet carrier escorts than slow BB’s, since fleet carriers were faster than “standard” battleships. (Of course, this only goes for the older generation of battleships, as the newer battleships were much faster than the old ones.)
3. The main secondary role that CVE’s undertook was amphibious support… which interestingly tended to be the role to which old battleships ended up being relegated. Thus, if you check out the Order of Battle for the Pacific Fleet at Leyte you see two fleets:
3rd Fleet: essentially the “Blue-Water Strike Fleet,” which included CV’s, CVL’s, new/fast BB’s, CA’s, CL’s, & DD’s
7th Fleet: essentially the “Brown-Water Amphibious Fleet,” which included CVE’s, old/slow BB’s, DD’s, DE’s, and transports.
I don’t think that the US had any of the Alaska-class CB’s operational yet, but when they did, they became part of… you guessed it, the fast strike fleet, not the slow invasion fleet.