There's going to be a problem with any Bitcoin-style currency once sophisticated algorithmic trading becomes widespread enough that compute time is always more profitably spent day-trading than mining.
Also, mining profitably requires special hardware built specifically for Bitcoin mining.
For bitcoin yes, but there are proof of work cryptocurrency systems out there that use CPU. And there are proof of stake systems out there that neither cpu or gpu intensive.
For a lot of people, cryptocurrency = bitcoin. But there's a growing number of crypto enthusiasts who see crypto as an constellation of cryptocurrencies, each with their own unique attributes and fundamentals, that complement (as well as compete with) bitcoin.
I'd presume that someone who is better versed in wall-street style algorithmic trading could speculate better than i what a mature cryptocurrency trading market would look like.
I'm curious to see what a mature market in this space looks like. It'll surely be different on a currency-by-currency basis, because volume, market depth, and fundamentals matter greatly and are unique on a per-currency basis. Time will tell.
As to whether profitable automatic currency trading competes with mining for compute time, I posit the following question to you: Are the two mutually exclusive? In a world with (1) scalable compute power via AWS, Digital Ocean, etc, and (2) both are profitable, why not do both instead of one?
This isn't hypothetical, the CPU mined coins aren't close to profitable with web services. And the people making profitable ASICs are using them rather than selling them because it's intrinsically more profitable.