Fjällräven is a very well-established Swedish brand that makes exactly this, and even have their own brand of wax. As far as I know, none of their products have any synthetic membranes.

Here in Denmark, "Fjällräven" is a household name to the point that it can be used to refer to their small backpack model.

[0]: https://www.fjallraven.com/

I enjoy my Driza-Bone coat — has been going strong for about 8 years now; just re-proofed it. Oil/wax-impregnated cotton is also easily repairable, unlike fancier materials.

It is a bit on the heavy side, though. Not really good for sports/cycling/etc, I wouldn't imagine. Also gets a bit ratty/threadbare wherever it gets repeatedly creased and un-creased.

But it really does work, and is long-lasting. I had previously been buying a new raincoat every few years due to some tiny crack in the waterproof layer that can't be easily fixed.

This is what I use because I've had it forever and it's cheap. It's heavy and high maintenance though. And if you're in wet conditions for hours it'll soak up a ton of water and just get even heavier, and take forever to dry.

There's probably no perfect solution here but this definitely isn't a direct replacement, though sure it's practical for a lot of applications.

You mean like Barbour jackets? They never went away. ;)

https://www.barbour.com