I disagree. I have no idea why one cannot figure out which button is which for just 5. We do it for numerical pads for cashiering without looking; I don’t know why it wouldn’t work for cars with large prominent buttons sticking out and pretty separate from each other. (Big question is whether the fingers really can easily press a button which might require some fine finger strength.)
Plus, today most commonly the front seat has been split to put the auto trans shift directly on the trans. While it is somewhat tactile, one often finds oneself looking down and right even to change from top to 1 or 2, just to ensure it’s in the right place. (Same applies to older column shift - one often has to ensure the 1 or 2 is properly engaged rather than the other Drive gears.)
You can certainly figure out a pushbutton interface, just like you can figure out any other poorly designed interface. It’s not that pushbuttons are impossible to use, just less natural.
I think buttons have two basic problems — ambiguity, and the fact that you have to anchor your hand to orient yourself. The action of pressing one button is only subtly different from pressing another. With a lever, the major actions are distinct. You slam it down until it bottoms out to put it in drive, for instance. No other gear feels like that. And because the lever itself is the anchor and reference, there is no extra anchoring step. The lever is simple where buttons are fiddly.