eah already are doing isn’t? I think they can very much co-exist and not just these too. I completely believe that down the line in next 3-4 years, I will be 10-15 Crypto Currencies that will be fighting for the top spot, so they all will co-exist and there is no reason why they can’t. The market is so big that it’s easy.
The real question should be, can altcoins co exist with bitcoin because bitcoin will be always here. Bitcoin has better support, a bigger community and a very active one. Altcoins including Ethereum are usually pump and dump coins, sure someone can make money with them by buying low and selling high because those have even higher volatility than bitcoin, but that's it, they are not as mainstream as bitcoin so their long life existence is not guaranteed compared to bitcoin.
i think the most efficient purpose of each coin will become evident; to me that is ETH being more transactional with bitcoin being a longer term, stable store of value. once we get more mature investors in the space, the price wont be quite so volatile. perhaps bitcoin will truly mature into a digital gold, the volatility now of all alts makes it anything but. unless you brought in so early on a coin that you will be in profit no matter what, you cant plan long terms savings goals with bitcoin; too easy to underestimate because of a price retraction, or waste time and overestimate because the price surged.