In 2001, a card back change nearly happened over (sigh) legal reasons.
Ever since the first Magic cards came out in 1993, the cardbacks have been unchanged. There have been a few near misses, such as when Arabian Nights was supposed to have had their own unique cardbacks or when Tempest was supposed to have different cardbacks for different draw triggers. But, well over thirty years later with a logo change and company owner changes, they have been a constant. Changing them now would severely hurt gameplay, with different cardback signaling different card ages and thus altering strategies.

The closest it has come was back in 2001, all over the Deckmaster box on the back of the card.
As the story goes, somewhere around the time of the Odyssey block, the company got serous with trademarks. Wit new buyers and branding going through a revolution for the internet age, everything that could get a trademark, would get a trademark. It was at this time a lot of legacy characters were being locked down and Magic itself getting protected. This included the cardbacks and 'Deckmaster'.
At the time, Deckmaster was still up in the air. In the 90's, it had been planned as an umbrella brand name for a planned series of different card games, Magic being the flagship. A few like Netrunner had them on their own backs, and in the early 2000's, there was still hope. Plus other games, like Pokemon, were going strong, and thus Magic needed to keep their uniqueness. So a trademark was needed.
But, as designers at Magic later said "The symbol was nearly added without thinking of the ramifications the change would have on the game, namely that players could cheat by using lands that didn't have the extra trademark and spells that did, or vice versa." This was huge enough an issue that Magic legal backed down on the matter right before printing.

Since the Deckmaster snafu, a cardback change has never really been attempted. In 2018, the new logo did spark Magic to create a reimagined cardback for funsies, notably without Deckmaster on it, but this brought in such negative feedback that the company has never brought it up again. Double-sided cards did play with this notion too, but players accepted those way better because they incorporated card changes and mechanics.
So, Deckmaster and the old cards live on to this day, despite the major change that nearly happened in '01.