I remember coaster brakes fondly. As an American kid, all of my bikes had them. What was great about them was that you can engage them so suddenly and forcefully that you instantly lock the rear wheel. If you did that on wet asphalt at high speed and jerk the bike just right, you could spin the bike around 180 degrees or more. It was a great day when I (accidentally) found that out. You can also do that somewhat on dry pavement, but your rear wheel is going to have a reduced lifespan.

I think that coaster breaks (and maybe steel frames) are better suited to kids who want to be rough with their bike. My wheels were never very true, and they would have rubbed awfully with rim breaks. (Disk breaks were unheard of on kids bikes then, and I think are still pretty rare now.) The main downside is that if you loose the chain, you loose all breaking power. That happened once to me, but thankfully there was a nice dirt ditch close at hand.