SS isn't too weak, it just doesn't benefit every job equally and has a diminushing return on the exact reason why it doesn't benefit every job equally.
And that reason is ogcd.
the more a job is dependant on their ogcd for performance (wether it is heal or dps), the less it will benefit from SS. SS doesn't affect ogcd (spare a few exceptions), so when your job has 30% of their dps based on ogcd, that's an issue. And as people mentionned, you have the issue of double weaving coming up at some point where you can't doubleweave without clipping.
You may also have rotation going off board depending on your SS where your gcd don't aligne properly (that was an issue for MCH back in SB)

This is why SS benefits heavily job which have their entire kit based on gcd (or most of it) such as BLM and SAM (and GUN if I understand right), or have burst window where SS help put an extra gcd WAR, DRK

So in short, if SS (and spell speed) would reduce ogcd CD or increase their damage, then it would become a much better stat for most job.
The effect would however have to be adapted to everyjob.
But that would be on a personal level, if SS would reduce ogcd CD, then some job would miss aligne their buff with other jobs and that wouldn't be good.
For instance, if a NIN with very high SS would end up with a TA on a 52s CD, maybe no other job in the party would be able to squeeze their burst window within that TA, making the benefit of that SS a bit counterproductive. (Same for DRG's jump or SMN Trance etc)

The most simple solution would be to just make ogcd damage scale from SS.