Brig only works as a third healer. She doesn't do enough raw healing to keep up a rein charging into the entire enemy team. It worked because you could plug Brig in as a third support who also functioned as a hybrid tank/added dps. And you can't replace lucio who is the necessary support character because of speed boost. So brig/lucio would never work to achieve a similar support role in 2-2-2. You needed all 3. Further diva's ability to peel and eat up reaper's damage was another integral part of goats (not just for reaper obviously as he was never meta). You can't just take that away and assume the rein zarya lucio will be able to function exactly as it did before.
I'll also add it isn't JUST the speed boost principle. Its having three tanks with large health pools coming at you with 3 support characters that can keep you up and speed down singe targets. Having 1 less 500+ health character and 1 less hybrid support character is a significant nerf to goats which is why you didn't see it replaced with a 2-2-2 equivalent. If it would have worked you would have seen the pros jump to it immediately after spending so much time learning the goat meta.
Which of course brings us back to the fundamental balance issue in Overwatch that both GOATS and double shield exploit: time.
Time is everything in OW. DPS, HPS, TTK, objective time, etc. Big health pools mean more survivability time. More survivability time means more time to do damage and fill the objective. So the goal, then, is not to out-damage the other team, but to out-survive them. Only when you're confident that you have the optimal strategy to survive the longest, then you focus on damage optimization. This is why Rein/Sigma is less viable than Orisa/Sigma, despite Rein having an objectively more versatile shield - it's harder to damage optimize.
Without 2/2/2, even with severe nerfs to GOATS heroes, the optimal strategy will always be either the biggest health pools, the strongest damage mitigation, the highest HPS, optimized for damage within these limitations, and then stacking as many of them as possible. I sincerely doubt that there would be any stable future meta from this point forward that follows a traditional 2/2/2 structure because the benefits of stacking survivability will always outweigh DPS efficiency. On a similar note, I doubt Shanghai's Cinderella trip-dips run in stage 3 finals would've lasted because they already had a less-than-stellar performance with that exact composition in stage 3, and triple-DPS dive (before OWL) was quickly subsumed by a two-tank dive with D.va. The principles of that fast, aggressive mobile damage comp would have eventually been supplemented with some kind of additional survivability.
2/2/2 isn't a magic fix, but it's a start. A basis to (hopefully) lower HPS, shields, and maybe health pools. Then maybe a reduction to DPS if necessary. Speed up the game where it needs it, and slow it down in other areas. That kind of balance could not be achieved where any nerfs or deficiencies could be compensated for with an additional stack of that role.