I'm pretty sure the main reason is aesthetics. And to be clear, I only saw fridges and stoves/ranges, no washing machines or dishwashers.
There are actually quite a lot of very nice smaller MCM homes in the area, Long Beach specifically has some great ones, and they are becoming fairly popular to renovate while keeping the original design. Some are quite small, by modern standards, and I think maybe the smaller size of the appliances are also attractive, but I haven't been appliance shopping much and I've never done a kitchen renovation so don't take this as gospel.
I just think that if someone has the money then a company like AGA makes cookers which I'm sure have looked exactly the same for the past 60 years - so you get the vintage look but modern efficiency:
Those AGA stoves do indeed look great. This was a few months ago so my memory is a bit hazy, but I believe the prices for the smaller 24" cast iron stoves were around $3000, which I found to be pricey. The AGA cast iron stoves in that size range seem to be $7000+ here in the US, although this was a quick look at pricing so I may be off. I can see why someone looking for that style might go with a restored stove.
On another note, I can definitely see that modern appliances like dishwashers or washing machines/dryers would be much better and more effective than older versions. I do wonder if there's any noticable difference in comparing something like an old cast iron gas stove to a modern gas stove?
In my experience, the main thing that distinguishes gas stoves is how precise the flame control is and how much heat you can throw off on at least one burner. (And, I guess, the flame pattern although given decently thick-bottomed pans it doesn't really matter much.)
But in general, a gas stove is a ring of flame. There's not much to it. You need enough flame and you need to be able to control it. If you have those two things, an old stovetop is fine.
Ovens are more complicated and I'm not generally a fan of gas ovens.
I'm pretty sure the main reason is aesthetics. And to be clear, I only saw fridges and stoves/ranges, no washing machines or dishwashers.
There are actually quite a lot of very nice smaller MCM homes in the area, Long Beach specifically has some great ones, and they are becoming fairly popular to renovate while keeping the original design. Some are quite small, by modern standards, and I think maybe the smaller size of the appliances are also attractive, but I haven't been appliance shopping much and I've never done a kitchen renovation so don't take this as gospel.
Edit: messed up formatting