"Monstrosity" can easily mean: "Magical Beast".
A "Beast" is comparable to a reallife animal, even if an amalgam of several reallife animals.
Meanwhile, a "Monstrosity" is a Beast-like creature with magical powers.
An Owlbear, a Griffon, and a Pegasus (if with naturalistic winged flight) can type as a Beast.
I think this, or something like it, might already be in the works.
If you look at the Influence action in the Rules Glossary, p. 27 of pt8, you can influence a beast or monstrosity making an Animal Handling (Charisma) check. The combination of them there, with the specific association of the monstrosity creature type with the skill Animal Handling, means that in some ways the groundwork is laid for the druid's shape change as well.
I would not be surprised to see a limited number of monstrosities in the PHB options for (at least) the Moon Druid.
Most likely candidates, were I to guess, would be from these:
CR 1/2: Cockatrice, Rust Monster
CR1 (flying): Hippogriff, Harpy
CR2: Shadow Mastiff, Centaur, Worg
CR 3: Owlbear, Basilisk, Yeti