Do modern analog sticks employ smoothing?

[thebigcheese]

Maybe that's the wrong question to ask, but a few of my controllers I have noticed some quirks with the analog sticks. It seems to me that some companies use some software trickery to change the way their analog sticks behave and I'm wondering if someone here has more experience with these sorts of things and could explain what's going on and why. When I test controllers, I'm using this web site, though there may be other ways of getting at this information. Here's what I mean:

• -The Switch Pro controller's sticks rest at exactly 0. I'm not complaining, but given the nature of thumbsticks, it seems highly suspect to me that they are actually that perfect.
  -My 8bitdo SN30 Pro and SN30 Pro+ both rest at just slightly off 0. In x-input mode, it's 0.00002, -0.00002. In Mac mode, it's more like 0.0032.
  -With the SN30 Pro, on older firmwares the stick would register movement in a square pattern despite physically moving in a circular motion. Additionally, moving the stick near the cardinal directions would snap (in software, not physically) the stick to that direction. In later software, this was corrected to true analog motion in a circular pattern.
  -With the SN30 Pro+, on all firmwares that I have tested the limits of the sticks motion change over time. If I move the stick around in a circular motion, initially it registers as quite a ways outside the 100% line. As I rotate the stick, the point gradually moves in until, after a few rotations, it registers as just about perfectly on the line and stays there until I turn the controller off and back on again.
  -On newer firmwares with the Pro+, the first time I move a stick in the X or Y directions, it snaps to 100%. This happens once for each axis. After that, it goes back to regular analog motion (with the above caveat about adjusting over time).
  -All of my DS4s just kinda go nuts. I think they worked fine previously, but lately the analog sticks just bounce all over the place. Probably not even related to the topic, honestly, as it's probably a driver-related problem, but it's still weird.
  -All of my XB1 controllers, meanwhile, seem to just register analog sticks normally, drifty sticks and all. They don't try to hide their imperfections.

Does this sort of processing add lag? Is it desirable in the first place? I don't really know anything about controller design and the like, so I can't really say one way or another, it's just kinda odd and makes it feel like something is wrong with the controller.