Is the destroyer obsolete as a ship type?
Is the DD as we have known it an "obsolete" ship type? What is the DD's mission? Is it a viable/useful platform for commerce protection? For commerce raiding? Would it make sense to replace it with a combination of LACs and/or FGs?
The destroyer is far from "obsolete," at least in the minds of the Manticorans. The destroyer's mission is the traditional mission of light units large enough to be independently deployed, small enough to be expendable if worse comes to worst, cheap enough to be built in large numbers, and powerful enough to stand up to other destroyers and light cruisers. The destroyer was never intended to fight heavy cruisers or above, and was never really survivable against those types. Essentially, a destroyer is used to protect and police commerce, and for scouting, anti-reconnaissance, system pickets, commerce raiding, and to screen heavier forces against harassment by other light units.
In terms of commerce protection, the destroyer (with appropriate upgrades to reflect changes in war fighting technology, like the Roland-class "spring design" I gave you a while back) is a unit powerful enough to compel an enemy to deploy heavy units if he wants to raid your commerce. Its job isn't to destroy heavy cruisers, but rather to make it difficult or impossible for anything lighter than heavy cruisers to get through to your convoys and to compel the heavy cruisers themselves to operate cautiously (by presenting the risk of potentially non-repairable damage to the raider) in order to dissuade attacks on individual merchant ships or convoys under destroyer escort. If an attack is pressed home by a heavier unit, the destroyer is also expected to buy time for the convoy to scatter or the merchant ships to evade, which usually equates to dying gallantly in defense of the merchies in the approved Saganami fashion. Obviously, the destroyer is also intended to completely deter attacks by outright pirates, and a ship like the Roland or even the Chanson-upgrade would be more than adequate to handle 90-plus percent of the pirates one is likely to encounter. When it comes to policing commerce, the primary function of the destroyer is to patrol, stop, and search. For [customs] work within a star system, it would make more sense to use LACs in this role, but beyond the hyper limit, the LAC's inability to enter hyper makes that impractical. Destroyers are ideal for stopping suspected slavers, for intercepting hyper-capable ships which attempt to evade inspection, etc..
For scouting purposes, LACs suffer from the fact that they aren't hyper-capable. They have to be transported to wherever they intend to perform their scouting function, and they cannot escape through hyper without first making rendezvous with and being recovered by their CLACs. A destroyer division or squadron dispatched to scout a star system has greater ability to deploy drones (since a destroyer can carry so many more of them), greater flexibility (the individual units of the division or squadron can split up to cover more area -- or scatter to evade interception -- and need not worry about rejoining before escaping into hyper if they run into opposition), much greater endurance (if, for example, a destroyer needs to "lie doggo" in a star system on stealthed listening watch for an extended period), and (in the form of the Roland, for example) a much greater ability to fight for information if it finds itself opposed by enemy light units. Not to mention the fact that a destroyer is considerably more survivable than a LAC. The LAC sometimes may be a harder target to hit, but it is also extremely unlikely to survive taking a single hit, and it has much less damage control capability.
In terms of the anti-reconnaissance and system picket roles, there are certainly specific circumstances under which LACs would do the job effectively, especially if available in larger numbers. However, it is virtually certain that it will never be possible to engineer MDM capability into something as small as a LAC, which means that they will always be at a severe disadvantage for long-range engagements. Enemy destroyers or light cruisers shadowing a task force or fleet are also logical targets for destroyer interception. Light cruisers might be better for that task, but destroyers will generally be available in greater numbers (assuming that the building priorities of the owning navy are constrained by available funds), will have better acceleration, and in the form of the Roland, at least, MDM capability. By the same token, a forward system picket of Roland-class DDs would be longer-ranged, more survivable, and possessed of longer endurance than a picket of LACs. Not to mention the fact that the DDs would be capable of independently fleeing the system in the face of overwhelming attack (thus enhancing not only their chances of survival but the chances that news of the attack will reach the relevant authorities) than CLAC-dependent LACs. And the same considerations which make the destroyer effective for the other missions discussed in this paragraph also make the destroyer well-suited to providing an anti-harassment shell around a task force or task group. Obviously, to some extent LACs could do the same thing, but, once more, in a post-MDM combat environment, the question of whether or not the screening elements have a long-ranged combat capability of their own takes on a certain burning pertinency.
I think that the above paragraphs should answer the questions about suitability for commerce protection and commerce raiding. I would simply add that the destroyer is always going to have a tighter personnel budget than a light cruiser, say, specifically designed for escort duties or, conversely, to attack the other side's commerce. A destroyer simply isn't going to have the capacity to produce large numbers of prize crews for captured pirates or for captured merchant ships. That doesn't necessarily equate to a lack of effectiveness in either role, however. Blowing pirates away is a perfectly acceptable means of dealing with the problem. If the destroyer has sufficient brig space to tuck away any pirates actually taken prisoner and/or enough life-support redundancy to support any merchant spacers liberated from their pirate captors, that really ought to be all it needs. Most pirate vessels aren't going to be worth buying into naval service, anyway, so once the crews have been accounted for, blowing them up rather than trying to man them and bring them home ought to be quite acceptable. As a commerce raider, a warship isn't really in the business of taking prizes, either. It's in the business of destroying enemy commerce. Under the rules of warfare, they're supposed to do everything in their power to safeguard the lives of the personnel crewing the vessels they take or destroy, but they aren't profit-seeking pirates, and they don't really care (unless, of course, there's a lot of prize money involved) what happens to the ships they stop as long as the other side is permanently deprived of those ships and their cargoes. For those purposes, destroyers -- and especially MDM-armed destroyers -- would work perfectly well, and they could undoubtedly be built in greater numbers and at lower individual cost than cruisers with the same types of weapons.
There are individual aspects of the destroyer's mission which could be performed equally well, at least under special circumstances, by LACs or FGs. But the LAC will never be independently hyper-capable, and the FG will never be capable of mounting worthwhile numbers of MDMs or of matching a contemporary, current-generation destroyer's survivability. The destroyer will remain the extremely useful generalist it has always been, and will neither magically become capable of taking on ships of the wall nor abruptly become the helpless prey of LACs.