For rain pants, there are both breathable pants that let sweat out and non-breathable ones that do not. The problem with the non-breathable pants is that your sweat can build up inside and then you will get wet underneath the pants anyways.
As non-breathable pants are still sold, what are reasons why some people might choose to use them? Is it simply a matter of cost?
As you are aware waterproof breathable fabrics can "wet out" reducing them to simply waterproof fabrics. That does not make wetted out waterproof breathable the same as waterproof non-breathable fabric. Non-breathable fabrics tend to be cheaper, stronger, lighter, and in some cases more water resistant (i.e., a higher mm H₂O rating) than corresponding breathable fabrics. Compare the differences between the high end fabrics used in Z-packs non-breathable kilt (1.0 oz/yd², 20,000 mm H₂O, and 15.5 N puncture strength) and breathable rain pants (1.92 oz/yd², 20,000 mm H₂O, and "don't look at it funny" strength).
If weight or durability matters and either sweat is not a factor or wetting out is a given (e.g., sailing or prolonged wet weather), a non-breathable fabric might be desirable. Sweat is heavily activity dependent and good ventilation can often mitigate the need for breathability. For really cold weather activities the effect of sweat can be eliminated through the use of a vapor barrier, but you will still want a waterproof shell to keep snow-melt from soaking your insulation.
You seem to have a specific outdoor activity in mind, like trekking or climbing. But what about water sports? A sailing ship deck would be the most obvious place. Sometimes you won't move much, but you wish to stay 100% dry.
In my experience waterproof breathable fabrics are only water resistant. Also notice that fabrics like GoreTex deteriorate with time and lose their water repellent qualities. A simple plastic trousers won't have this problem.
There are several uses, but regular strenuous outdoor leisure activities aren't really among them.
Breathable gear only goes so far - there comes a point when the best gear you can afford will result in getting very sweaty. This point is a function of temperature, humidity, price and activity level. If you're consistently going to pass that point, non breathable gear is cheaper (much cheaper in the long term as membranes degrade) and still keeps the wind off.
They're often used by those working outdoors doing fairly light duties, such as directing traffic or otherwise mainly standing. These are often high visibility. More strenuous outdoor workers may well use heavy duty poorly breathable versions.
They can be kept in a vehicle as emergency wear to keep in case of breaking down or worse. These may never be worn so it's not worth investing in something expensive. They also seem more waterproof than at least cheap breathables if you're actually sitting or kneeling in water fixing something. A similar use is car camping, when you may need to go out in the rain to tighten ropes or pegs, but would avoid going out in the rain otherwise.
In the UK climate, and many other places, it's often worth carrying rain gear for even fairly gentle walks that take you more than a few minutes from shelter. You'll be a lot drier and warmer in cheap waterproofs than none at all, which is why compact ones are widely sold in national park shops etc. (I keep a pair in the van that were an emergency purchase in such a shop)
The non-breathable pants are usually considerably cheaper than the breathable ones. That can make them a better choice for activities that stand a good chance of ripping holes in the material, glissading down icy slopes for example. Far better to rip your $25 non-breathable pants than your $125 Gore-tex pants.
The non-breathable cheaper wet-weather protection is useful for when you must sometimes go outdoors in heavy rain to do essential jobs, but not for very long.
Long enough that you would otherwise get soaked, but not long enough for the lack of ventilation to be a problem.
Non-breathable waterproof garments are basically polyurethane plastic at the surface. This has one very big benefit in that dirt doesn't stick to it much, and what sticks will usually come off with just water.
So they're good for uses such as:
Trekking in muddy conditions. Just hang them overnight to dry and yesterday's muck falls off.
Children's use. A high-tech fabric will not stand up to daily washes for very long.
Agricultural and other jobs where you'd get excrement on your clothes.
After all, getting sweaty is a discomfort but it can be tolerated.
To ride a motorcycle, for example, you will never chose breathable fabric. If you have to wear rain pants, temperature is such that sweat is almost never an issue and you want your garment to be as waterproof as possible. Also, you want to be sure not only water but also mud, grease, dust, etc. is kept off your under-layers, hence the use of a fabric as less porous as possible.
As a cyclist, I expect to get wet if I'm riding hard in the rain. But if I'm wearing something waterproof -- breathable or not -- the (cold) rainwater will be kept separate from the (warm) sweat, and I'll be warmer.
And if I'm not riding hard, I'll be dry longer in the non-breathable stuff, because water vapor can pass through the breathable layers in either direction.
Aside from the practical differences aside, i.e. breathable lets sweat out, but tends to only keep rain out temporarily, breathable fabrics are typically made of 'forever chemicals' which might cause cancer, in very small doses, and stay in your body for a long time. 'forever chemicals' don't tend to break down in the environment. See for example https://www.theguardian.com/environment/2022/jan/26/water-resistant-products-toxic-pfas-study for an article about water resistant products and PFAS ("PFAS" means "Per- and polyfluoroalkyl substances").
So, one possible reason to use non-breathable waterproof pants is to not absorb PFAS into one's own body, or distribute them into the environment around oneself. This doesn't mean one cannot obtain breathable waterproof pants that don't contain PFAS; nor that everyone will choose to take this path, but it's one possible reason why someone might choose to use non-breathable waterproof pants.
