Counter-missile fire control issues and counter-missile pods
The main problem with all the current suggestions is simply that the fire control issues are much more significant than people seem to be allowing for.
The RMN has already addressed some of this in its shipkiller pod designs, in which they are now (as of the introduction of the Invictus-class into service) using a single missile in each pod as the telemetry link to all the missiles in that pod, thus effectively increasing their ability to handle multiple numbers of missiles. The problem has always been in the numbers of individual channels available, not in the data processing capability of the mother ship, and this cuts down on the numbers of channels required by a factor of about six.
But the problems of wedge interference -- the "gunsmoke" and "funnel smoke" of the Honorverse -- is another matter entirely. You can't get "through" it, so you have to get around it (if you can) it you're going to add multiple control platforms. The LACs being used in missile defense under the Foraker Doctrine are basically formating in "holes" in the wall of battle. They can be fitted into much smaller intervals than larger vessels (even destroyers) because their wedges are so much smaller. And if there should happen to be a case in which their wedge impinges on a capital ship's, the result -- while fatal for the LAC -- will not significantly endanger the capital ship. IOW, the risk of ship wedge fratricide is acceptable, on a cold-blooded tactical/strategic level. But the critical point is that from where they sit in the formation, they are using their CMs in direct fire mode with their own dedicated control channels, broadcasting through the open rears of their own missiles' wedges and using their spatial displacement from the capital ships (and, especially, from the point at which the pods left behind by an accelerating wall actually launch) to avoid the "holes" being cut by other ships' CMs. (Shipkiller broadsides, wherever possible, are programmed to "climb" or "dive" above the plane in which missiles must approach the wall in order to attack the relatively narrow target of the open sides of the ships' wedges. That means that, to at least a large extent, a wall can avoid blinding itself with its own fire but that it would actually create additional problems for additional control platforms displaced above or below the main wall.)
At present, the only use of CM pods is to thicken normal point defense when battle damage has eliminated normal CM tubes. That is, the ship launching them has "x" amount of control capability. Its launchers are configured to allow it to fire a total number of missiles requiring 1.25-1.50 times "x" CMs in a single salvo. This is to allow it redundancy and to allow "hand off" to other platforms when possible and practical. If hits begin taking out CM tubes, then the density of the defensive salvos it can fire obviously drop. The canisters of CMs which can be fired from conventional launchers are intended to put a "fast pack" of missiles sufficient to make up losses from the normal tubes into space. They are not intended to throw up a solid wall of missiles which can't be adequately controlled in the first place. The notion that a ship would launch shpikiller-sized pods of CMs in order to thicken the defensive fire thus runs afoul of the fact that thickening it by that huge a number would tend to enormously reduce the effectiveness of the defenses by seriously degrading the ability to steer the missiles to intercepts in such a control-adverse (if I may use the term) environment.
The nature of the CM itself only adds to the problem, because its onboard target seeking is much less sophisticated than that of a shipkiller. It needs more control for the intercept because the sheer size and power of the impeller drive engineered into it puts too much squeeze on its (much smaller to begin with) internal volume to permit the same self-targeting ability as a shipkiller and its targets are already harder to lock up (courtesy of all the penaids loaded into them, decoys, small size of target, etc.) than the target the more capable shipkiller is looking for to begin with. So you have greater need than ever for fire control from some more sophisticated platform, but the greater the numbers of CMs you send downrange, the more that control ability is restricted.
So the short answer is that I don't think any Navy in the Honorverse is currently likely to be particularly interested in dedicated antimissile platforms. The generalist designs already in service are capable of putting out all the defensive fire current generation control systems can handle, anyway, without significantly reducing offensive firepower (especially in the pod designs) and without making them dependent on the presence of the specialists. Unless/until there is a major change in the fire control limitations available to a fleet commander, this is unlikely to change.