When you're doing a three point turnaround with traffic bearing down on you it's nice not to have to deal with fiddly buttons. Or when you're maneuvering a pickup to line up with a trailer hitch which can take some back and forthing. Or anytime you need to shift quickly and by instinct and feel.
Over time you'll gain some muscle memory even with buttons just as you would with any poorly designed tool or interface, but it will never be as natural or intuitive as a shift lever.
A bank of buttons is simple and cheap to make compared to a shift lever mechanism. That's what car makers would use if they could get away with it, but it's just too poor of a design in terms of its operation.
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.)