tl;dr Higher integration and faster CPU's killed them.
In the early days of PC's most EVERY peripheral was provided by an IO expansion card save for the keyboard. My 386 had a 16-bit multi-IO ISA board that provided the essential coms ports: ATA, floppy, serial, parallel. You purchased a VGA card and then a sound card. You had at least 2 or three ISA cards because your motherboard was taken up by all the CPU, FPU, RAM, and essential control logic chips. My second 486, a DX2 66MHz, had the ATA, serial, parallel and floppy ports on-board which amazed me as it eliminated a whole ISA board. (Now everything fits on a single silicon die...)
Early on-board audio was usually a sound card soldered the the motherboard. Then Intel developed AC'97 which integrated standard audio into the south-bridge. Coincidentally that made Microsoft's life easier as all the PC's they were running on would use this standard meaning all they had to do was provide AC'97 drivers and everyone with an Intel machine had sound. No more competing 3rd party audio api's from Creative, et al. it was all Wintel. PC builders could now provide multimedia PC's for cheaper prices with audio by default. Also, USB happened which allowed people to plug in things without opening cases and fiddling with circuit boards which is alien to many.
And as CPU's became faster, the need for dedicated DSP processors to handle audio processing or synthesis is eliminated. You can now run a whole DAW complete with synth, sample playback, effects and mixing in real-time on a cheap general purpose off the shelf computer with no special hardware.
In the early days of PC's most EVERY peripheral was provided by an IO expansion card save for the keyboard. My 386 had a 16-bit multi-IO ISA board that provided the essential coms ports: ATA, floppy, serial, parallel. You purchased a VGA card and then a sound card. You had at least 2 or three ISA cards because your motherboard was taken up by all the CPU, FPU, RAM, and essential control logic chips. My second 486, a DX2 66MHz, had the ATA, serial, parallel and floppy ports on-board which amazed me as it eliminated a whole ISA board. (Now everything fits on a single silicon die...)
Early on-board audio was usually a sound card soldered the the motherboard. Then Intel developed AC'97 which integrated standard audio into the south-bridge. Coincidentally that made Microsoft's life easier as all the PC's they were running on would use this standard meaning all they had to do was provide AC'97 drivers and everyone with an Intel machine had sound. No more competing 3rd party audio api's from Creative, et al. it was all Wintel. PC builders could now provide multimedia PC's for cheaper prices with audio by default. Also, USB happened which allowed people to plug in things without opening cases and fiddling with circuit boards which is alien to many.
And as CPU's became faster, the need for dedicated DSP processors to handle audio processing or synthesis is eliminated. You can now run a whole DAW complete with synth, sample playback, effects and mixing in real-time on a cheap general purpose off the shelf computer with no special hardware.