Or to put it another way:

Yes, that's gravity saying, "I'm the boss of this."

My point was that, even if your claim that the chainring pushes the chain toward the rear derailleur were accurate, which my examples showed it isn't, whatever happens to the lower span of the chain has no effect on front shifts.

That said, your final statement ("front shifts go smoother and make the equipment last longer when you momentarily soft pedal while the chain is switching over") is indisputably accurate.