"If I had said, “I will speak thus”, behold, I would have betrayed the generation of your children" (73:15). Why didn't he say it?

The verse gives its own reason: speaking so would have "betrayed the generation of your children" (73:15). Betrayed is bagad, which Brown-Driver-Briggs gives as "act or deal treacherously". The psalm doesn't say who "the generation of your children" are beyond those words, or whom he would have told. It does set down what he had been thinking: "Surely I have cleansed my heart in vain" (73:13). And speak in 73:15 is sapar, which Brown-Driver-Briggs gives, in the form used here, as "recount, rehearse, declare". The same verb is in the psalm's last line, where he says what he will tell instead: "I have made the Lord GOD my refuge, that I may tell of all your works" (73:28). The psalm doesn't say more than that, and these notes don't either.