Is there actual economic value in trading crypto currency? When you invest in a stock, you're helping the company to raise capital.

It seems like trading crypto currency is nothing more than putting money into a pool (market cap) and trying to predict when other people will put more money into the pool. No economic productivity happens here except for money changing hands. Is there actual any value in trading coins or is it just money changing hands?
Yes, there is.

People who trade currencies (or commodities, for that matter) broadly belong to two groups - those who actually need to convert one thing to another; and those who hope to buy low and sell high for profit.

In Bitcoin's case, typical examples of the first group are an individual who receives his salary in USD, and converts the USD for BTC to use it; and a business which receives payment in Bitcoin, and converts to USD to pay its suppliers. In both cases, economic value is created by enjoying Bitcoin's advantages; and in both cases, trading BTC/USD was needed to allow activity that would be impossible or less efficient without trading.

The second group is simply people who trade BTC/USD for profit, and often come out with the same currency with which they went in. To be successful, they need to buy low and sell high - and if they manage to do that, they are actually providing a service to the first group. Since buying drives the price up and selling drives the price down, buying low and selling high keeps the price stable at some midrange. This makes the price more stable, and reduces slippage costs, thus making the usage of the currency more efficient. So they are also creating economic value by making it easier to use the currency for commerce.

This is true even over long periods of time. A Hodler who buys a bitcoin for $1, and only sells decades later when the price is $1M, is helping the economy by giving the currency a push when it is nascent and underappreciated, and only realizing her gains once Bitcoin has reached its potential.

Of course, a dumb or unlucky trader can buy high and sell low; in this case, he is actually adding volatility to the price, and creating economic harm. But he will also take a loss himself if he does that. As long as the trader is making a profit, she is creating economic value.