Destroyers were pretty general purpose at the end of WW2. Then the USN decided to do away with light and heavy cruisers and make the destroyers do the tasks. They also added a new role: ASW. At the apex of Cold War organization, there were ASW destroyers (DD), anti-aircraft destroyers (DDG) and light cruiser sized general purpose ships (Destroyer Leaders [DL]). The goal was for each one to do it's own taskings.
With the USN's success with TV-guided munitions and anti-radar weapons, the line was blurred and it was planned to mount the new guided weapons (Harpoon) on every ship. This gave every ship - regardless of role (ASW/AA, etc) - the ability to do multi-tasking. This was a force multiplier as the Soviets had religiously followed our example and created their own families of destroyers for ASW, AA, etc.
Funding (then as now) was based on fear and it was widely believed that the only chance the Soviets had was to saturate us. As the USN's SM-2 missile system could only engage six targets at once, this put the USN at a disadvantage. If the Russians could launch seven aircraft, they'd conceivably swamp a USN ship. The DL's (Coontz/King Class and new nuclear California Class) would mount the new extended range (ER) SM-2. This went from a range of 75nm to 150nm.
The Russians responded by adding more aircraft to their fleet. The USN was back to square one. It was actually the Australians (not the Russians) that first came up with vertical launch. This meant that a DDG could now throw all of it's SAMs in the air, defeating any swamping tactic. Since the reds could swamp us with planes, why not subs as well?
So ASROC was configured to be fired from the vertical launch MK-41 system. As a "trial" one was mounted on USS Spruance. The problem is that the MK-41 bank held 64 weapons. The existing ASROC launcher/magazine held 24 weapons. This meant that a Spru-can could conceivably go to sea with 64 weapons. Problem is - the USN didn't have 64 ASROCs for each Spru-can. So the other 40 slots tended to be filled with Harpoon, Tomahawk and SM-2ER's. But Don, the Spru couldn't launch SM-2. Correction: the Spru couldn't *guide* it. It could launch them all day. Just couldn't guide them.
So your friendly Coontz/Tico would order a launch from the nearest Spru and then once the birds got in the air, the ship giving the order would take control of guiding them. At that point, the Spru's became cruiser-like in their firepower. With the emphasis on the ER version of SM-2, the Adams, Sherman and California Class ships had no use. So a more capable replacement was sought. Enter the Arleigh Burke.
Now that they have embarked helo's and full ASW dipping sonar, they are the true replacement for the Spru's and also for the Tico's as they retire.