> One could definitely take parts of MPEG1 and MPEG2 to create a new good enough codec for many use cases.

Well people did exactly that - and they named it:

  - MPEG-4 Part 2 (also known under names like DivX, Xvid, ...)
  - MPEG-4 Part 11 (also known as AVC, H.264, ...)
  - VP8
  - VP9
  - AV1
  - MPEG-H Part 2 (also known as HEVC, H.265)

Those are all codecs that build on and extend what MPEG-2 is.