If you deviate from the specs it wouldn't work with MP3 decoders, so what would be the point?
Lame --alt-preset standard is really excellent and very rarely trips up. If it does, it's not usually too bad, so don't hesitate to use it if you need MP3 compatibility for portables etc. Problem samples that still affect Lame APS badly are now very rare or have only very subtle artifacts. In this forum we're looking for them and we're very critical so you could get the wrong message.
A few options let you go outside the spec while remaining compatible with
some decoders (e.g. --freeformat allow bitrates above 320 kbps and is not limited to the same bitrate steps as compliant MP3, IIRC)
Sure, MP1, MP2 and Musepack .MPC have better time resolution - good for transients, and Musepack is more efficient.
As I understand it, Musepack was developed to get around the limitations of MP3, MP2 etc., as you suggest, so in a way it's already happened (although it uses a different method of encoding - it's not an MDCT-based hybrid codec like MP3 but works more like MP2)
Time resolution is improved and the sfb21 issue isn't a problem, and VBR is better supported (native timing and seeking information without needing a Xing tag). MPC is also gapless - matching the exact number of samples in the original WAV, and it's more efficient (lower average bitrates at the --quality 5 --xlevel than Lame APS). But it needs a different decoder to MP3.
(Use the search button if you want to know why these things are problems in MP3)
Ogg Vorbis attempts to solve it without using any of the known patents that impede MP3 and MPC. It's amazing at low bitrates and I have high hopes that GT3 will come close to MPC quality and bitrates in the transparent quality/safe joint stereo) range of q values.