You can blame the lack of uptake of MPEG-2 in the personal computing space on the license terms set by the MPEG LA, which charged patent licensees an amount based on the number of encoders and/or decoders they wanted to ship [2], and because DCT codecs were too slow to decode on CPUs until the mid-1990s. There were competitive proprietary codecs that could be licensed more favorably and performed better. These got built into codec-agile platform media stacks like QuickTime, Video for Windows, and later, Real and Flash, and these stacks would gain support for newer codecs as the technology progressed.

It wasn't until 1999 with MPEG-4 that the licensing situation made MPEG codecs an option for desktops again, by which point other proprietary DCT codecs were widely deployed. Both Microsoft and Real dabbled with tech that came out MPEG-4, but it wasn't until that H.264 became decodable by mainstream computers that everyone finally settled down around an MPEG codec. Then, Google bought On2. (But that's a long story for a different thread [1].)

Here's some more detail for this thread:

H.261 pre-dates MPEG-1 by a bit. H.261 was compiled by the ITU-T chiefly to support video telephony, because the predecessor codec H.120 was conceptually neat, but practically garbage. H.261's design choices and JPEG's design choices factored heavily into MPEG-1 Video, and while the MPEG-1 standard also delivered a program stream and 3 techniques of audio compression, it was hardly broadcast-ready: it was missing a transport stream for unreliable media, and it was missing support for interlaced video. These deficiencies were rectified by MPEG-2 in 1996.

In the early 1990s, DCT-based video like MPEG-1 was too slow on contemporary mainstream desktop hardware, so people developed vector quantization codecs that would allow realtime playback: Cinepak, Indeo, MS Video 1, Smacker, and TrueMotion S. Some of these saw a lot of use in video games, and some were picked up by OS and platform-based stacks for multimedia, like QuickTime, Video for Windows, and then later, Real and Flash. Those platform stacks were designed with codec agility so that more advanced codecs could be switched in as developments came along. But correspondingly, good candidate codec needed to have a favorable IP situation for widespread deployment, so codecs were often homegrown from skimming contemporary sources (including standards), or licensed from smaller companies instead of the alternative: paying the MPEG LA for a license per decoder deployment, and then still having to procure decoder software.

Later, processors became more powerful and you could decode DCT in real time. In 1996, H.263 came out as an improvement over MPEG-2/H.262 at low bitrates. Other codecs followed suit and we ended up with RealVideo, Sorenson Spark in Flash Video, and VP3. The importance of OS-delivered or runtime-delivered media stacks rose; Real, QuickTime, Video for Windows, and Flash. These platforms would go on to dictate the containers, the video codecs, and audio codecs that were supported, so they had a dominating influence on multimedia on personal computers for the next decade.

MPEG-4 came out in 1999, which brought both MPEG-4 Part 2 (-> SP, ASP, DivX, Xvid) and H.264/AVC. The former was a bit of an improvement over H.263, while the latter had great potential but mainstream processors were too slow once again.
Microsoft cribbed MPEG-4 Part 2 to make a version of a Windows Media Video codec, RealVideo did the same, and DivX and later Xvid rose to prominence in the early 2000s. The latter two gained notoriety for being used for DVD rips and filesharing; one could convincingly compress a 480p main title from a DVD in MPEG-4 Part 2 to ~700-1000 MiB, 700 MiB would fit on a CD.

Right around this time, Microsoft was showing off their latest WMV to prove you can have HD movies on a DVD. But content owners wanted bigger disks with better DRM, in part to make filesharing more of a hassle, and were leaning towards H.264 as the codec, so Microsoft got their latest VMV standardized as VC-1, and based their marketing on easier decoding, interlacing support, and a favorable patent situation. They got their VC-1 written into the HD-DVD and Blu-ray standards alongside H.264 and the aging MPEG-2. But it turned out there are patents on VC-1 after all and a patent pool was set up by the MPEG LA just the same; and then hardware finally caught up to decode H.264, so everyone settled on an MPEG codec at last. Briefly.

[1] https://news.ycombinator.com/item?id=15845114 [2] https://www.mpegla.com/programs/mpeg-2/license-agreement/