PS2, Gamecube, Xbox, Emulation
The Playstation 2 hit shelves a year later featuring backwards compatibility with the original Playstation.
This new incarnation basically included a full working version of the original hardware which made it a practically trivial task.
Sony must have faced the same debate Nintendo did during their Super Nintendo development.
The Playstation was hugely popular and available pretty cheap. The
Dreamcast was off to a slow start so maybe there was some fear that
gamers were satisfied with Playstation and not interested in dropping a
stack of cash for something glitzier. Whatever concerns existed about
keeping the Playstation alive were ignored and the Playstation 2 went on
to become the most successful game console to date.
The Xbox and Gamecube were the last entries to this gaming generation,
neither were backwards compatible for obvious reasons. The Xbox had
nothing to be backwards compatible with while the Gamecube was
Nintendo's first departure from the cartridge format.