I remember reading someone speculating that knowledge of how to cast them was mostly lost, with those who still know generally unwilling to teach others. What's the in-universe story behind banned cards, if there is one?
To my knowledge, none of the media put out by Wizards of the Coast provides thematic justification for the banning, or restriction, of specific cards. In a general sense, some keyword abilities or effects only appear in specific regions, because they are generated thematically for those portions of the verse.
Cards are banned solely for mechanical reasons, to limit the dominance they would exercise within one format or another. The intent is to avoid tournaments where the banned cards start to define the meta, to the extent that there is only one deck played, or one deck and a deck designed to beat it.
That is specifically highlighted by Wizards of the Coast on the
Banned and Restricted Lists
One key to the continued health of Magic is diversity. It is vitally important to ensure that there are multiple competitive decks for the tournament player to choose from. Why? If there were only a single viable deck to play, tournaments would quickly stagnate as players were forced to either play that deck or a deck built specifically to beat it. In addition, different players enjoy playing different types of decks. If there are plenty of viable options to play, there will be more players at more tournaments.
To help maintain the diversity and health of the Magic tournament environment, a system of banned and restricted lists has been developed. These lists are made up of cards that are either not allowed at all, or allowed only in a very limited manner.
It’s important to note a couple of things: First, these lists apply only to Constructed formats and not Limited formats. Second, the banned and restricted lists are format-specific, so a card that is banned in Modern may still be legal to play in Standard.
Banning a card is uncommon. Announcements for changes to the Banned & Restricted lists are done all together on the Monday after a new set’s Prerelease, to go into effect with that set’s release. This way, the formats you play change as infrequently as possible.
For specific guidance on why a card was banned, you would have to look through the Magic the Gathering Article Archives for Banned and Restricted Announcement's. Googling with the terms "banned", "restricted", "announcement", and card name will get you the pertinent announcement.