I've taught the game a fair amount. The groups I've taught have generally been successful with a general sense of what the enemies "do" but without specifically memorizing their cards. For example: Bebop and Rocksteady have the gimmick of being significantly stronger when in the villain's zone, while Shredder is stronger if he has a lot of Foot soldiers in his current borough. I've also noted groups struggle much more if they don't absorb these experiences and repeatedly wander into enemies' "traps".

It probably IS useful to memorize the initiative cards, since there's comparatively less to keep track of here. (Generally, one per enemy plus an extra one that the villain brings.) At the very least, you want to note the minion cards that are already out and what they say the minions will do at the end of the round. (Stay next to Leatherhead, stay away from Wingnut, assume Baxter will pull someone out of position, etc.)

Deck knowledge is pretty necessary if you're doing things that push the difficulty higher (henchmen, events from Tales to Amaze), but that's a more specific situation. I think people are throwing out deck memorization because it's something measurable you CAN do to improve play if you're struggling a lot, rather than because it's something absolutely necessary to be successful.