The thing is, if Starfleet was able to catch up to Khan with more than one training vessel, then he shouldn't really have stood a chance, given how Kirk ultimately was able to defeat him even with just a training vessel. If there's a point of frustration I have with the TOS movies in general, it's that except for TMP and TUC (the first and last, amusingly enough) Our Heroes are handicapped and we don't get to see them at their full potential.
TMP: New Ship
TWOK: Training Vessel
TSFS: Seriously undermanned.
TVH: BoP
TFF: Malfunctioning Ship and undermanned.
TUC: Everything up and running, finally!
TMP: New Ship
TWOK: Training Vessel
TSFS: Seriously undermanned.
TVH: BoP
TFF: Malfunctioning Ship and undermanned.
TUC: Everything up and running, finally!