Jesus said "the Father is greater than I" and prayed to the Father. Doesn't that make Him lesser?

You are not inventing it; He did say it, and He did pray to the Father and submit, so take the texts at full weight. And the submission really is everywhere in the Gospels; you are right to see it. And you are right that if "greater" meant "lesser in being," the whole thing would unravel.

But "greater than I" read as a confession of inferiority misses what the submission is for. It is the faithful human party of the covenant being kept at last. Every covenant needed a faithful human and none had ever come, Adam grasped to be like God, Israel rebelled within forty days. Yeshua (Jesus) does the opposite: "the Son can do nothing of Himself, but only what He sees the Father doing" (John 5:19), "not My will, but Yours" (Luke 22:42). That is not inferiority speaking. It is the human side of the covenant walked perfectly, the trusting son the Garden was always meant to produce. When He says "the Father is greater than I" (John 14:28), He speaks from inside that human role, ordering Himself under the Father the way a faithful son does, the way Adam would not, and out loud, on purpose, to teach us the posture. The Word in flesh submitting is not God reduced. It is God showing us, in a body, what a human being was always meant to be.

Do not take it from me. Read John 5:19 and Luke 22:42, and ask whether they sound like a lesser being or like the one faithful son who finally kept the human side.