Coaster brakes work well enough (but definitely use a normal front brake as well as the front brake will always stop a bike in a shorter space) and I have two ancient ones in my stable. They would have been an optional extra at one point on most British roadsters and anyone who has ever attempted to stop a rod-braked roadster from speed in heavy rain or snow would appreciate it's all weather capabilities.
The trick is to become good at keeping the pedals in the right position when freewheeling as the brake can only be applied forcefully from certain positions and also when coming to a complete stop as you can't spin the cranks backwards to get the right starting position when stopped.
The OP is probably referring to something like my late 1930s single speed Humber with an Eadie Coaster Hub (these hubs were made between about 1895-1940 when the BSA hub factory was bombed. Geared versions were also available). The Eadie was one of the first of it's kind and works slightly differently to more familiar ones like the Sachs Torpedo - there is a clutching mechanism which engages when you back-pedal and a reverse thread activates a cam which engages the brake shoes on a small drum on the left side of the hub shell. It's not much different to typical drum brakes still found on the back of small cars except that the brake shoe is brass and is supposed to be oiled (oil port provided but oil never stays in it for long - hence the oily mess). My brake drum is worn out of spec but I got it working again by soldering pieces of steel on to the cam actuator and filing it to suit so the shoes engage more. There is still a lot of metal on the drums so I don't think it will crack and anyway, it doesn't do many miles in an average year. God knows where I'd find a replacement brake drum.
You can see the single front rod brake. The axle was actually bent but one from an old MTB wheel had the right thread which is why it's so long. I should really cut the excess off I suppose.
The Sachs Torpedo on my 1960s Batavus is typical (I think) of all modern ones which uses a split tapered cone which slides along the axle on the reverse thread and clamps the inside of the hub shell and it is important to use high melting point grease when rebuilding these as they can get very hot.