Successes like Spock visiting his childhood, Kirk facing off against Orion pirates, and Kirk and Spock joining an impossible mission to save the galaxy justify failures like the crew turning into children, the center of the galaxy being full of magic, and the Enterprise computer becoming a dangerous prankster. The TOS Rewatch does an overview of the animated series.
Best of all, the series enabled Trek to get a bit more alien in its landscapes and creatures, going even further than they went in the third season, where they were heavily constrained by budget. (Though, of course, that was half the reason why they went more alien in season three, but whatever.) It was worth it to give us more far-out crew members like Arex and M’Ress and nifty non-humanoid aliens. Plus, the animated series did something neither the live-action TV series or the movies had the balls to do: put Uhura in charge of the ship, not once, but twice!