Almost no one makes 3/8" inset cabinets anymore because the hinge hardware is difficult to source, and the door tolerances are too tight. The doors tend to have the usual problems of sticking in summer when the humidity swells the wood. 3/8" inset is actually the worst type of door for that. Worse than traditional inset cabinetry is. And the hinges are not adjustable, like almost all modern hinges are.

Well, I've had a very different experience than most, I guess. My cabinets never had trouble closing, even in the most humid conditions. You've stated "almost no one" which means that someone still does... I wonder who?

There might be about 5 old farts in the country who could still do cabinets like that without massive issues. It is more exacting. The market moved away from it over 40 years ago.

Wow, I sure wouldn't call a craftsman who can make a solid cabinet with strict tolerances "old fart". As more and more of these men die off, we're losing a lot of knowledge and quality craftsmanship. The market moved away from this because most likely the guys at the top could make more money easier and give the consumer a crappier product with less hassles on their end. In the end, kitchen cabinets end up being junk instead of something that a homeowner can be proud of. I know from re-ordering several "off" cabinets that most of what passes for "good" quality these days can't hold a candle to cabinets 40 years ago. It's a pretty bleak outlook for things to come, IMO.

The market moved away from that because the doors had problems sticking in anyone's houses that didn't have strict humidity control. And the doors were mostly plywood, with not the prettiest edge details that were left exposed. The same stickiness still holds true for traditional inset, which is much more poplar. You might be able to get some of what you want with traditional inset. You'll just be missing the 3/8" lip that overlaid the frame.