I'm sorry to have to say this but your math isn't solid. At all. You say skins take up 2-3kB of space and then round down to one kB for your estimations, when you should be assuming every skin is taking up the max amount of space allowed. Also, I don't quite know what shady place you by you 2 terabyte hard drives from but a quick google search shows that they can cost from $100 to nearing $200. Which last I checked was anything but 'almost free'. So either you have been buying from some place that is seriously underselling their product or you just have so much money that dropping $100 dollars on a hard drive is nothing to you. Either way, for most people, even a 1 terabyte hard drive is pricy.
I'm not saying the idea is bad I just don't think you've thought out the amount of space this would take up throughly enough. But fix your 'math' and I'll decided if I think this is viable.
You seem to be right on the math, but wrong(ish) on the HDD. They can cost that much, but you can get one for as little as $70 on sale. But regardless of that, we aren't talking about what we can afford, we are talking what Mojang can afford. The people who have made tens of millions of dollars on the various versions of Minecraft so far. They can afford a simple 2 TB HDD and seeing how they are a business, they probably have all sorts of various connections to other businesses and companies to get a discount. Hell, if they put a tiny request on their blog that they needed one their fans would probably mail 10 of them.
Well, maybe not but they can afford it easily regardless.
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I like the concept, but I would turn it off regardless. Mainly because it is incredibly hard to make a smooth animation with about 10 frames so this would really only be good for flashing lights on suits or small details. But it could work very well with this suggestion (not advertising, very related and makes skins much more versatile):