Another nice option, especially for streetwear, is Ventile cotton: https://en.wikipedia.org/wiki/Ventile
Ventile clothes without nasty water repellents applied on top are generally marketed as EtaProof.
Ventile is an exception to the "rule" that "cotton kills" (in the cold).
Especially great is for staying dry is double layered ventile, which is now free of flourine chemistry for extra waterproofing (older iterations used PFAS as an extra waterproofing coating.)
The cotton breathes, it's more durable than gore-tex or off-brand knockoffs (stressed PTFE), and it doesn't make annoying "swish swish" noises either, which is helpful for bird watchers and other folks that want to move quietly in nature.
There are two major disadvantages: cost and weight. A ventile garment is many times the price of a similar ptfe garment, especially now that the original gore-tex patents have expired. And it's also many times the weight.
However, let's be honest, if you can afford ventile, you probably can drop 3 pounds of fat through the additional time you will spend outside, lengthen your healthspan and lifetime, and use the garment long enough to pay for the several "waterproof" ptfe garments you would have gone through in the same time.
It was also worn in the summit of Mt Everest by Edmund Hillary as it is a great windstopper.
It has nothing to do with regular cotton.
With the margin of error in the outdoord being as small as it is, I’d trust synthetics or wool that will always work vs the risk my cotton isn’t treated recently and reaches failure.
Ventile works it's magic by the combination of long fibered cotton, thigtly spun thread and a close weave. The result is a fabric that after some time swells in rain by absorbing water, and then becoming saturated and impermeable(ish) to further ingress of the wet stuff. The inside will feel damp, but not wet. Wool as a base layer is of course an excellent counter to this. And, all the while excess body heat is shed quite effectively. When at rest, put on a wool or fleece 2nd layer, just like with a synthetic shell.
A compromise, yes. But the greatest advantage over 3L membrane etc. in my opinion is the ruggedness and durability, "experienced wetness" beeing alike. And in the high mountains, boreal or a mid-winter climate with months of stable sub-freezing tempratures, this is a supreme choice for your outer shell. Sweat converted to frost forms on the outside of the garment, instead of the inside as it is want to do in a 2L or 3L. Brush it right of, and carry on.
In the 80’s wool hiking gear used to be around for this reason too. I’d never feel appropriate recommending cotton for anything serious, any season.
If you look at people that do hard labor or outdoor guide work in extreme hot climates around the world- they all use cotton or similar plant fibers. All of the concerns about cotton come from it cooling "too well" and that often simply isn't an issue. Synthetic and wool stuff is also just not very durable, and incredibly expensive.
I say this as someone with decades of outdoor experience, an ex-boy scout, etc. who used to be a hardline proponent of "cotton kills" in all outdoor conditions. I learned the hard way that I was wrong after being proven wrong time and again in real world conditions, by people with more experience than me that were able to keep functioning in extreme heat better than I was.
The trench foot etc has nothing to do with cotton or synthetics, it’s being wet for days and days. I’ve seen people get it. I’d trust synthetic or wool socks to dry faster and hold their shape (blisters are just as bad) than cotton any day. Also nobody is overheating (or breaking the bank) in Darntough socks.
Your assumptions on moisture and temp management are based on an assumption of environmental control that doesn’t exist in the outdoors. The margin of error is very small for slipping into chilly and then cold as hell, and it happens quickly. Lack of durable synthetics (which I’ve never had give out on me, inspect your equipment prior to leaving lol) vs durable but risky cotton is a silly trade off, in this light.
Heat stroke, the actual type that’s bad, gets prevented from pounding salted water and ice sheets. For it to get this far such that it happens, no amount of sweaty cool cotton will help it.
I say this as someone who learned the hard way as well or watched others did. I am an Eagle Scout, was in a combat branch in the army for a while, been in very hot places for very long, seen trench foot, heat cats, cold cats galore.