You have to understand that “obsolete” is much more of a recent understanding culturally. In the 80s it was still far more common to see appliances as things you bought for life and to see electronics like a television, computer, hi-fi, etc. as appliances.

The oversaturation came not just from a plethora of games but also from a severe lack of quality control and from Atari and other companies rapidly releasing new consoles, that weren’t exactly upgrades to the previous consoles, to a market that wasn’t interested in replacing the system and games they just bought while dumping support for the previous console. Atari is most guilty of this and an attempt to reduce inventory and increase price led to the now famous ET carts buried in the desert story you may have heard about.

By the time Nintendo was ready to release the NES in North America they did so through toy stores and marketed it as a toy and not a computer for games (one example of this is the board inside the cart only takes up about 1/3rd the space, they made them bigger for kids to handle in NA compared to the Japanese version called the Famicom). As well, they had extremely strict quality control guidelines with things like the Licensed by Nintendo seal appearing on approved games and accessories, and bans on retailers that sold unlicensed games. It took a couple years but this approach paid off. They also didn’t drop the NES when the SNES was released with the last official NES game (Wario’s Woods, also the only NES game to get an ESRB rating IIRC) coming almost 5 years after the SNES came out.