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When that Senche attempts to maul you with Medium Armor on, it's a lot tougher to get to the juicy parts. You run by one naked, you'll start to slow down when all that red fuel leaks out of your big open wounds.
Usain Bolt should know the answer, I think he tested everything as the professional runner. I think some clothing provides some level of comfort, so it is worth wearing no matter of result. As for ESO, well it's just a game, nothing is true, everything is permitted.
Certain articles of clothing actually make you faster. In competitive swimming, bodyskins had to be banned as they were made of a special material that reduced friction and drag compared to bare skin; even shaving off all one's body hair was not as effective as a swimmer simply donning specific swimsuits. And shoes definitely speed up running on land due to absorbing shock and acting like a spring to propel the body faster. So while lighter clothing certainly helps more compared to wearing armor, it doesn't always make sense that someone completely naked would be faster than they would with clothes on. I personally think that Light armor should have been granted the speed bonuses that Medium got, seeing as how Medium has no penalties, but that's just my 2 cents.
This raises the question to me whether you can call an Argonian or Khajiit without clothes actually naked? One would assume that they don't need shoes to run faster.
In the real (re-enactment anyway) world heavier armour on the ends of limbs really hurts your stamina and your ability to do things but most chest armour has little effect on anything but long term stamina. You can run fast in a chainmail shirt, but you'll get really really hot and sticky far faster. On the other hand wear gauntlets and wave your arms around and it'll ache *much* sooner than without.
I do miss all the funny comments that Skyrim had when you walked into a merchant, or past a guard with nothing on.
While encumbrance is a staple in older sandbox MMORPG's, ESO has no encumbrance system. Would be cool, but I doubt they are going to waste time, resources, and money implementing it.