So you think whichever coin is considered a store of value wont necessarily have the highest market cap?
There's arguments for and against Bitcoin being a store of value, for example, with most classical economists saying that it isn't, but this is really depending on whether you're considering the micro-fluctuations of the price of Bitcoin over weeks and months, or the macro-trend over the longterm of years. It's hard to argue that over the course of any randomly-selected 4-yr period that Bitcoin isn't a store of value and that won't store value with a very high probability.
This is true with many other cryptocurrencies as well, and while there's for sure a correlation between price-reliability and marketcap, what's a better predictor is actually age. Older cryptocurrencies (at this point in time) are more easily identified as price-positive, and therefore above price-stable, over the longterm, (and so can be argued to be good stores of value).
It means that the market places a solid amount of weight behind the longevity of a cryptocurrency when it comes to future predictions of price, and this weight is actually over-representative compared to what it actually means in a practical sense. ie. You don't need to have created a cryptocurrency in 2013 in order for it to be more likely to hold its value, and conversely that a cryptocurrency created yesterday won't necessarily be outperformed by even Bitcoin, Litecoin or Ethereum in this sense.
I don't think people will use Tether as a store of value.
People already are though, in fact that's exactly the reason that the most traded cryptocurrency in the world today is Tether. Not to generate profit, but to act as a proxy store of value without there being a fluid/free way to move cryptocurrencies to "real world" money, like USD, which is what most everyone is measuring their success and failure in cryptoasset trading against, because that's how they and anyone else will ultimately reap the rewards from trading - buying real shit with real money in the real world.
At some point the real world won't be USD or EUR, and we'll be able to buy 70% of everything we can now with (insert cryptocurrency) - so Tether and other fiat-pegged stablecoins will be largely obselete. This is why I think that while Tether is popular today, reality will catch up with them in the coming years, as being able to maintain your trading wealth in comparison to USD/other fiats won't be relevant anymore.
Tether is for sure already a store of value, more so that Bitcoin or other speculative cryptos obviously, and it's actually the only reason that Bitfinex have made the pretty outrageous amounts of revenue that they have from Tether up until now.