"Don't you have to push down on the stick to get it in reverse?"
Nope, there have been odd shift patterns over the years.
Both of my Subaru Outbacks go into reverse by pushing the stick all the way to the right and down, which does seem to be defacto standard with the adoption of the 5 speed transmission. There's no lockout, though, unless it's passive.
I can't remember 100%, but I seem to recall that my Plymouth Sundance was all the way to the left and UP.
I've driven cars where to go into reverse you had to push a little button or tab on the shifter. I THINK that the early Vegas had a collar that you had to pull up with two fingers.
Supposedly on some cars you can (or could) get, special order, a dogleg gearbox in which reverse is all the way to the left and up, with first in the down position (where second would normally be).
All four of the cars I've bought have been manual transmission, but I think the next one I get is going to be an automatic. A few months ago I went from the beltway in Washington, DC, to Frederick, Maryland, (about 40 miles) in horrendous stop and go traffic. By the time I got to Frederick my left hip and knee hurt so bad I thought I was going to puke.