Of course there are many non-verified games that run fine as well.
For comparison, the Switch has somewhere between 5,000 and 10,000 games.
Source: Wikipedia lists about 5000, Nintendo says “over 5000”, but this website claims 10,880. Part of why the Moby Games website lists more is because it lists multiple versions of a game as separate games (Xenoblade DE is listed 4 times for example).
Yes this is my biggest complaint of the ecosystem. Many games are difficult to play with the controller even if they are verified. For one: I wish there was an easier way to change the joystick acceleration curve for each game.