On the monster manual, page 11 you can find the special grapple rules for monsters which explain why a DC is provided for grapples performed by monsters.

As for the Water Weird's constrict limitation, note that there is nothing stopping it from using constrict repeatedly on the same target every turn. 

While it is true that drowning takes a while and a creature is unlikely to be killed by drowning during combat, the grappled (and restrained) creature is likely to continue to take damage every turn since as you noted, the Water Weird now has advantage when attacking it.