I am confused about all of this.
Well, there's 4 places you could, in abstract, place one of these on a compressor.
Exhaust (air out):
1) Air outlet to the hose/brush/tool. That's an enclosed line, so an open-sided, non-in-line filter like this wouldn't go here. There are moisture filters like the normal in-line bottle type that use sintered brass/bronze bead media like this in place of the normal fiber/foam piece, however. That may be a good sign as to this type of media's filtration ability, or they may just be made for other compressed air applications that have different filtration needs. IDK.
2) The bleed valve. This is the bit that abruptly goes PSHHHHHHHH every time the motor shuts off after topping off the tank. Its job is to ensure neutral air pressure in the line between the motor and the tank (and thus in the motor guts) whenever the motor isn't actively running, as back pressure in the motor when it's not running can damage it. There's no way to put a muffler on these (and it doesn't need filtration), as the button that opens the valve is inside the air outlet itself (like with the air valve on a car tire) so you can't cap or enclose this air outlet without preventing the valve from operating when/how it's supposed to. Large industrial compressors may use a different valve setup/type for this, and thus might be able to use a muffler. IDK. Small household/garage ones like most of us use can't though.
3) The tank drain valve. This is the spigot at the bottom of the tank. Its job is to allow you to drain out condensed water that may have pooled in the bottom of the tank. It can also be used to vent tank pressure, but this can also be done through to tool/hose outlet. Putting a muffler/filter here would interfere with the ability to drain water through it. You could in theory install a forked manifold here so it'd split into an air drain and a water drain, each with it's own valve, and the "air" end with a muffler. Personally, I just use the tool/hose end to vent the tank air, only opening it a little so it vents slowly and quietly, and only use the tank drain valve for draining water while the tank is not pressurized. If I wanted to be able to vent FAST and quietly, I'd use a manifold with a muffler on the hose end rather than the drain valve.
Intake (air in):
There's only one of these: where outside air is sucked into the motor to be compressed. It needs a dust/particle filter to prevent airborne particles from getting into the motor where they can become "sand in the gears". Most compressors come with a fiber or foam based filter that screws onto the inlet, and also acts as a muffler (a surprising amount of compressor noise comes from the intake, not the outlets). These aren't very good mufflers though. In fact some of them can act as resonating chambers, making noise worse. These can be easily replaced with a sintered brass/bronze muffler/filter like the ones we're talking about.
In this context, a sintered muffler filter has some notable advantages: it's much more space efficient, and it works much better as a muffler. Fiber/foam filter/mufflers are probably cheaper, but also probably not by enough to meaningfully raise the MSRP of the compressor, which makes me suspicious as to why compressors aren't shipped with them instead of fiber/foam ones. There must be a good reason. The only reason I can think of (by process of elimination) is that they don't perform well enough as filters. I might be wrong though: this is just guesswork on my part.
All the sintered filter/mufflers I've seen are advertised as "exhaust" mufflers. I've never seen one labeled as an "intake" muffler. This ties into the above question about their filtration ability.
Also, these listings tend to be vague about the kind of machinery they're meant for. It's possible they're not intended for air compressors in any context, but rather for other pneumatic or combustion driven industrial machinery. IDK.
Basically what I'd want to know is:
A) what kind of specs does an intake filter for a compressor need to have (what type and size of particles does it need to reliably catch), and
B) are these sintered muffler/filters capable of meeting those specs.
If the answer to the latter is "yes", then I'd say go ahead and swap out the fiber filter on your compressor for one, regardless of why they're not put on these compressors stock (i.e. the reason is probably economic, not practical). If the answer is "no" then it's better to stick with the stock filter, unfortunately, and seek a different way to limit noise.