Because Atari, Nintendo, and Sega were stupid.
The Jaguar was at the beginning of Gen V, and was pretty much dead on arrival. Atari had been a declining presence as early as Gen III, but Gen V sealed their fate.
Nintendo stubbornly stuck to cartridges because of faster load times and less piracy. This killed a lot of third-party support.
Sega completely botched the North American launch of the Saturn. It was $100 more than the PS1 and had an unplanned early launch. Third-parties all but ignored the Saturn, especially in the West. Not to mention Sonic Team never got Sonic Xtreme or another flagship Sonic title out.
I'm not acting like the PS1 doesn't have other merits, but it succeeded on the competition being tone-deaf and stupid. That's why the PS4 sold much more than the Xbox One, and far far more than the Wii U.
Lifetime Sales Predictions
Switch: 144 million (was 73, then 96, then 113 million, then 125 million)
PS5: 105 million Xbox Series S/X: 60 million
PS4: 120 mil (was 100 then 130 million, then 122 million) Xbox One: 51 mil (was 50 then 55 mil)
3DS: 75.5 mil (was 73, then 77 million)
"Let go your earthly tether, enter the void, empty and become wind." - Guru Laghima