Obviously, khajiit and argonian PCs should have the option to equip footwear for game balance purposes. As amazing as Morrowind was, the lack of a choice to use certain piece of equipment comes off as a bit dated (the game is getting close to 20 years old!). But we all know there is a difference between lore and gameplay. For example, there's no way that Skyrim in lore has cities with only a couple hundred people in them at most, and there's no way that the entire land of Skyrim has only a handful of farms and a handful of hunters and fishers to supply food. To add to the confusion, the very shape of those two races changes between games, something which is sort of explained with the many different breeds of khajiit, but even that raises some issues. What are the odds that every single khajiit in a game will be of that same breed? There's no one "right" way to render a cat or lizard-person, so this isn't an attempt at pushing one specific design, although I have to admit that the digitgrade over-sized "clown feet" they had in Morrowind was more than a little odd.
ESO seems to try to have it both ways, with argonians and khajiit having sandals or at least open-toed footwear (to make room for their claws, probably), something they often have for the bosmer, along with sandals as part of the standard gear for some redguard and Imperial sets of clothes. As one might expect, most of those sets apply to light, medium, and heavy armors, which are almost by definition meant for soldiers, guards, and adventurers, not the common populace. If anything, this question is more a matter of what the civilians of the argonian and khajiit populations would use, as adventurers need all the protection they can get. Would those races even develop footwear in the first place? Even if they could do it, would they if it didn't give them any advantages in their native lands?
As one might imagine, the kinds of clothing a certain group would develop by itself would be done to match their environment. This is why nords don't use the same clothes as redguards. Most of the playable races in TES are relatively similar, basically being humans or humans with slender frames and/or pointy ears. The beast races throw a huge wrench into that setup. In their case, biological differences between themselves and the humans/elves (notwithstanding that some Khajiit are elf-like in appearance, at least in lore) would also play a role in their clothing choices. For khajiit, their fur would make it harder to use heavy clothes in an already-warm environment, especially if the khajiit in question has fur like a cat species which comes from a cold environment. I don't know how the thickness of their fur is determined (by breed? By family line? Do the moons affect it?), so if anyone knows, feel free to share. As for argonians, they might get cold easily in a country cooler than Black Marsh, Hammerfell, or Elsweyr, but would they even need sandals in Black Marsh?