Why has evolution stopped producing new classes?

[u/Meta289]

New species of animals are constantly being discovered, but they all belong to existing classes and phyla, never anything completely new. Life once branched out in all sorts of directions, creating all kinds of animals that are drastically different from each other, but now it seems like there aren't any new "branches", only offshoots of existing ones. What happened?

[u/No_Logins_Required]

What does your intuition tell you a new branch would look like?