While grappling has its limits, I can think of several fun ways to make the monsters use it.
a) A giant crocodile bites an opponent, grapples it and sinks back to the bottom of the river, biting the poor restrained character with advantage and trying to drown it while he holds its breath.
b) A vicious balhannoth grapples a target and teleports along with it a few times using legendary actions, each time farther from the group.
c) A flying creature grapples a adventurer close to a ledge, pivots and drops it down the abyss...
All of these situations happened at my table in the past few months, and now grapples are feared by my players. Granted, in the two 1st cases, the restrained condition was imposed along with the grapple, but in the third example, not.
I wish my players would come to think to use it more often themselves, but I think PCs have a little more to lose than mobs, in terms of action economy, in trading up a damaging attack for a grapple.