Each sound card speaks a different "language." In the days of MS-DOS your program had to talk directly to the sound card, so you had to add the "language" of the specific sound cards you wanted users of your program to be able to use.

With more complicated OS's (Windows, Linux, OS/2), the OS speaks a single "language" to programs, and under the hood there's a "translator" (device driver) that works for each sound card.

Basically it stopped being a problem when PC's started using OS's that would "do more" for programs, including talking to the sound card. In turn this new kind of OS was enabled by other underlying trends:

• Computers gained more memory, more disk space, and more processing power, there's enough spare performance to add extra layers/complexity to the OS and software
• PC CPU's gained the ability for an OS to run in a "privileged" mode and "be in control" of the computer, isolating programs from each other and the hardware
• Larger floppy disks (1.44 MB) and CD-ROM's made it easier to distribute large pieces of software
• Microsoft made deals with PC makers for Windows 95 to come standard with new PC's
• A larger market [1] means it becomes financially feasible for a company to pay higher dev costs to create more complicated software, as they can predict they will sell enough to recover the dev costs and make a profit.

[1] Before 1995-ish, PC users were kind of like MMO players or VTuber watchers today, a large community but a bit niche / nerdy and not quite mainstream. From 1995-2005 PC's became more like smartphones today, considered essential devices for the vast majority of the population (at least in the US and other advanced countries).