A lot of players may not realize this, unless they are playing a druid, or someone with polymorph, but 5e has a problem. DMs who do a lot of world building know it, and once I point it out, it will drive you up a wall. The Beast type is nonsensical, and if you make it to high levels, its empty. A ranger who reaches 14th level and picks Beasts as his new favored enemy should probably get a stern warning from the DM (or more positively, a bunch of homebrew).

At the time of publishing, the most powerful official beast is Traxigor, at CR 12. What’s a Traxigor you may ask? Well he’s an 18th level wizard in Baldur’s Gate, Descent into Avernus who, thanks to how WoTC wrote the stats shows up in most online monster filters and counts as a beast because he’s polymorphed into an otter. Your DM probably isn’t going to let you to polymorph into that one, and its pretty specific on if you’ll ever encounter him for your favored enemy. The next best are the CR 10 Sky Leviathan from Planeshift Kamigawa, and the CR 10 Gishath, Sun’s Avatar, from Planeshift Ixlan. Both, more likely to see play than our friend Traxigor, but probably not in your DMs bag of tricks either. Especially not if its a player introducing the option, and not as a random enemy by the DM. The first “reasonable” option is the Tyrannosaurus at a massive CR 8. And even that’s a dinosaur, which enough people complain about in D&D that it might be safe to assume you can’t really pick it. A giant ape may be unique, and if your DM is a true purist, you may be stuck topping out with the CR 4 elephant, if you’ve seen one.

Nonsensical. The Beast, and Monstrosity type have a ton of overlap, and there doesn’t seem to be a strong distinction between the two. The Giant Ape is a Beast. The Giant Frog (Froghemoth) is a Monstrosity. The Stirge is a Beast, but the Grick is a Monstrosity, and neither are Aberrations. There’s no clear line, except stuff that’s “Kind of magic” can be a beast, and stuff that’s “Kind of more magic” is a monstrosity. This would be less of a problem if you had things like a Roc (Monstrosity) switch over to flesh out the Beast team a bit, but they didn’t. We have obvious extremes (Horses are Beasts and a Remorhaz is a Monstrosity), but outside of that, its like they picked out of a hat. “But Krusk,” you ask “didn’t the Monster Manual give definitions?” Sure, let’s take a look.

Beasts are nonhumanoid creatures that are a natural
 part of the fantasy ecology. Some of them have magical
 powers, but most are unintelligent and lack any society
 or language. Beasts include all varieties of ordinary
 animals, dinosaurs, and giant versions of animals.

It seems like it should be straight forward, and yet somehow Froghemoth aren’t beasts. If they aren’t unintelligent, lacking in society, a giant version of an animal, I don’t know what is.

Monstrosities are monsters in the strictest sense frightening
 creatures that are not ordinary, not truly
 natural, and almost never benign. Some are the
 results of magical experimentation gone awry (such
 as owl bears), and others ,are the product-of terrible
 curses (including minotaurs and yuan-ti). They defy
 categorization, and in some sense serve as a catch-all
 category for creatures that don't fit into any other type.

So its just literally a catchall for everything else? Got it.

My proposed fix is simple.

New Subtype. Beasts

I recommend folding Monstrosities into the existing Beast type. The Beast type now has two subtypes that may or may not be applied at DM discretion. Beast (Animal) and Beast (Monstrosity). Any existing features in that make a function call to the Beast type should reference the Beast (Animal) type and anything mentioning Monstrosities should reference the Beast (Monstrosity) type. If your DM is lenient, they may let you combine the two for most things, like favored enemy, polymorph, and wild shape. I certainly recommend it. 

The broad rule of thumb for DMs to determine which gets which subtype: Anything with any magic powers at all is a Beast (Monstrosity) and anything with no magic powers is a Beast (Animal). Yes, Rocs get to be animals.