That's probably influenced by d&d 4e
Multiattack being a single action sounds unique to D&D 5e. As you mentioned, ad&d had multiple attacks, so did 3e. But 4e had a similar concept for multiple attacks in a single round.
3e had a different concept of both 2e and 5e, in that you had actions separated in standard actions, move actions, swift actions and free actions (among others), and for a creature to make multiple attacks, they had to take a Full-Round Action, which combined their standard and move actions together. So a staggered (only one standard or move action per turn) creature couldn't make multiple attacks, for instance. For players and monsters, it worked exactly the same way, with very few exceptions that allowed you to make more than one attack using a standard action.
You can read more about this on the answers for how multiple attacks work on d&d 3.5.
4e had a different concept altogether from 3e, where you had powers that required a certain type of action to use, and each class and creature had their own set of powers available, requiring different types of actions. Rangers, for instance, can start at 1st level with the ability to shoot two arrows in a single standard action. While there were monsters that could make many attacks in a single standard action, like a Marilith that could make six weapon attacks once per encounter, and then once again when it first hit 50% hit points.
Even so, when a creature, like the Marilith, had multiple attacks in a single power, they listed the stats of that attack as a separate (at-will) power, and then mentioned that it can use that attack again n amount of times by using this other power.
If anything, this design choice on 5e was influenced by the action economy of 4e, where some monsters could make multiple attacks in a single standard action and still use their move action to go around the battlefield like the player characters.
As to why players can replace an attack for a maneuver and not monsters, that seems like an unnecessary nerf to monsters but probably justified in the intent of 5e's developers to make heroes to be special. So monsters and player characters have different mechanics to avoid a monster locking down a hero by chaining grapple checks, which doesn't really sound fun from the player's point of view.