Always_Ask_Questions,
“how do you explain Bava Basra 21 that explicitly describes the trial and error process that Tannaim (or earlier) used to come up with a working educational system?”
That is a very different case. Pirkei Avos are proverbs disseminated by the great links in the chain of Torah transmission over multiple generations. It literally represents the wisdom of our mesora. The gemara in Bava Basra is describing a series of takanos that the sages made in response to a specific situation – the deterioration of Torah transmission to the young during the Second Temple period. It was not that nobody ever knew how to teach children before and the sages in the Second Temple had to go figure it out. Our mesora was אב מלמדו תורה, as it says in krias shema: and you shall teach them to your children. This stopped working due to yeridas hadoros and the stressors of foreign occupation, and Rav Yehuda (via Rav) credits Yehoshua ben Gamla for making the takana that saved Torah from being forgotten by the Jewish people. Note that the gemara is clear about what the problem was, and why the sages were enacting each takana. By Pirkei Avos, GH is imposing her own reasons for the statement that appeal to her own values system.