Lots of Chryslers from the late '50's and early 60's had push-button automatic transmissions. There were a couple of AMC cars from around the early 1960s that also had it. The Edsel had it too - located right on the steering wheel. And the Lincoln MKZ from this decade had it as well, on the center stack next to the radio (and may still offer it, but I don't know that for sure since I haven't sat in one since about 2013). There are probably even more, but those are the ones that immediately come to mind.
As for why it's not more common - the first reason is simply cost. It costs more to make buttons connected to actuators etc., do something than to have a lever physically attached to the transmission do the exact same thing. If you save even $5 per car with a lever rather than a button-system, you've just made $500,000 in extra profit over 100,000 car sales by simply going with a manual lever instead of the more complex button setup to do the exact same thing.
Another reason is probably safety and reliability, at least on older cars. With a lever, if all hell breaks loose and you HAVE to get that transmission into or out of a gear for some reason, it's safer to rely on a manual lever connected directly to the transmission than on a button that may or may not work based on if the electrical system is damaged, an actuator is damaged, the computer controlling it all is damaged, or any other number of variables that simply aren't present when you simply attach a rod directly from the transmission shift mechanism to the shifter handle located inside the car. In theory it might seem to make sense to combine more functions into a single device (like one screen that can control lots of functions), but in reality combining lots of simple functions into a single device is usually better for handheld devices like smartphones than in big mechanical devices like cars in my opinion anyway.