Wax. Wax holds coats the inside of the up, mainly because it’s easy to do. Straws are a much different animal when you’re talking about cylindrical fluid dynamics. Now you’ve got suction bringing the walls of the tube in if the fluid/drink can’t rise in the straw. The hydrostatic pressure of the drink also increases as potential energy is put into it with the suction and it requires even more pressure from the straw sidewalls in order to not collapse. This is why you see cylindrical straws (even dispersal of pressure) and corrugated straws to increase structural integrity, especially with the bend of some straws. This means you can’t have a “weak” material that will crumble under pressure, the effect that occurs when you soften a material as a byproduct of the waterproofing process.
A square straw would just flatten, like a freezer pop or gogurt under suction, but you aren’t SQUEEZING the drink up the straw tubes. With all of this together, wax constructs flow requiring larger straws, but then the larger straw might not fit all applications. The companies that make paper straws don’t actually care about saving the planet, they are just marketing a competing product to plastic straws that doesn’t achieve the objective but breaks down faster. The cup doesn’t have to provide structural integrity in the negative direction (from suction), only the positive pressure of the fluid in the cup, allowing the waxed side to provide a water-tight seal on 2 sides (the sides and the bottom), and the outer rigid structure of firm paper cup can keep the form of the shape from exploding.
Edit- more context
A paper cup meant for liquid has a plastic or wax coating. The straw probably doesn’t.
Depending on your local jurisdiction and what exactly the cup uses there’s 3 ways to deal with it: Garbage, recycling or compost.
Some recycling facilities can deal with a product like a paper cup. Some can’t and for some it’s too expensive.
Cities that have modern industrial compost facilities can actually break down these into compost, assuming that the plastic used was of a compostable variety.
If all else fails, it goes into the trash.
Most paper cups are lined with something to make them water resistant. Usually plastic, occasionally wax. If you put hot liquid in the wax ones, the wax become part of the beverage. If you put cold liquid in there plastic ones, the condensation on the outside eventually soaks the paper to the point it will crumple if you try to pick it up. A waxy straw would lead to waxy teeth. A plastic coated paper straws defeats the intended purpose of the paper straw.
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