Stropping definitely doesn't remove material. It heats the edge which aids in deforming it back into a more preferable shape as you press into the material (leather, canvas). If material was removed it'd embed in the strop and damage your edge, either by chipping or just uneven action.

A strop with paste is a different beast, IMO. You didn't traditionally use a paste with stropping. I'd bet the rise of pastes, which seem kind of gimmicky, is related to a loss of traditional expertise and knowledge about the function of the strop. Relatedly, because of the rise of safety and cartridge razors, people are accustomed to extremely sharp edges. A traditional straight razor shave feels harsher--more pressure and pulling--than people expect. Utterly unrealistic depictions on TV and film don't help, either. For years I thought I just really sucked at sharpening and honing my traditional straight razors (one of which is a very expensive Thiers Issard given as a gift), but after several traditional straight razor shaves at barbershops, which were consistently harsher than the hairshaper and Feather I normally use, and the discussion with that one barber who was an expert on straight razors, I realized it wasn't my poor blade sharpening skills--well, not just my poor skills. Traditional straight razors just were never meant to be as sharp as manufactured, disposable blades, and can't be unless you want to spend more time maintaining the blade than actually using it. Similarly, if you're constantly removing material the blade won't last very long as it depletes beyond a useful profile. Contrast that with wood planes and chisels, which tend to have very deep, thick profiles because of the need for more frequent sharpening and material removal; you need that depth so the angle of attack diminishes less as it shortens, otherwise you'd need to compensate with a more fragile bevel, which would just accelerate the process.

Steeling might remove some material, especially when used on harder steels, but in the particular case of pressed stainless I don't think so. (But would be happy to see evidence to the contrary.) Traditional stainless steels (not new alloys with, e.g., molybdenum) are relatively soft. It's part of the reason why they're considered more resilient than traditional steels. They tend to have higher shear and tensile strength than non-hardened steels; they'll deform more before they break so they absorb energy better. So, for example, a stainless steel screw is closer to the resiliency of nails in terms of sheer strength than regular screws. Moreover, a pressed knife almost by definition needs to be made of relatively soft metal. One of my first jobs was working in a kitchen where we used horribly cheap pressed stainless knives for preparing chicken strips. After slicing a bag of chicken breasts you could actually feel the edge rolled over, like a letter J. (EDIT: rolled over is a poor description; if it were completely rolled over deformation by steeling would never work given the direction of the stroke. Note that the letter J isn't upturned on my font.) We'd always have to steel the knifes at least once or twice a shift. If steeling removed that material you'd have metal burrs everywhere, including in your food.

Maybe steeling traditional Western chef knives does remove material. But if so I wouldn't be surprised if the benefit is in tearing the edge, effectively making a micro-serrated edge that works better than an otherwise dulled edge. Still, I'm dubious that's the primary function if it is at all. Everything I've read and experienced (as a home cook, at least) is that Western knifes traditionally use softer steel, and steeling is for deformation/reformation of the edge without removing material.[1] Steeling a traditional Japanese knife, or especially a straight razor, is verboten because of the potential for chipping, macro or micro. I'd never shave with a straight razor that had been steeled, though I confess I've never tried that specifically.

That said, I admit the purpose and mechanical action of steeling is debated. I see conflicting discussions (not formal material) all the time, including from professional chefs, and I try not to discount people's experiences. Plus, it's not uncommon for the reality of something to differ than the theory even when the same result (e.g. easier cutting) is obtained. And times have changed. Modern alloys have different properties than traditional steels, so it's entirely possible the steeling action is different on many newer knifes than older ones.

[1] Indeed, IIUC, the very conclusion of the research article suggests that if steeling worked by cutting material rather than deformation, you'd end up with significant microchipping and by definition a less sharp and uniform edge.