The drying cabinet is actually a Finnish invention [1] (although apparently preceded by a US patent that never took off). It was popular in Scandinavia for a while, and you still come across homes from the 50-60s that have them, but they're no longer popular now that most people have automatic dishwashers. My family has a mountain cabin in Norway, built in the 1950s with no dishwasher, that have these, and they're very handy.

[1] https://en.m.wikipedia.org/wiki/Dish_drying_cabinet

I never have enough dirty dishes to do a full dishwasher run, and I find I need new dishes before I've run a load, so now I just handwash and use the dishwasher as a drying rack.

Very nearly every home in Finland has one these still.

In Italian it is called "scolapiatti", it may well have been patented in the US and be a Finnish invention (in the form suspended over the kitchen sink), but in Italy it has been a traditional tool since dishes were invented, it used to be an outside piece of furniture, more like a basket:

https://maisonderose.wordpress.com/2014/03/17/cera-una-volta...

http://www.lasoffittaretro.it/classico/48-scolapiatti-in-fer...

until houses had water (and thus sinks), I believe that as soon as sinks were installed in kitchens, the one or the other form of "scolapiatti" became in use, this is an early, primitive, type:

http://www.comune.sangiorgiodellarichinvelda.pn.it/fileadmin...

And this is another example:

https://www.picclickimg.com/d/w1600/pict/192394042552_/AAX-P...