I agree with all the items in the Larry’s post. Remember that the shaving coming out of the plane is not the goal.
I do not think a precision lapped plane sole is important because all my pieces are planed, then scraped, and finally sanded before they see the final finish. Plus I work in a garage in Texas, and +/- 40F temperature swings or greater within a day are common. No piece of iron will stay “flat” in that environment.