Bitcoin does solve the issue of being able to electronically pay people you may not trust, but so does PayPal. Bitcoin transactions are slow to confirm, you have no protection as a buyer to perform a chargeback (for example, you buy tickets for a concert that turn out to be counterfeit) and the price of Bitcoin is extremely unstable. Bitcoin also is not really free of transaction fees, either. You will pay a fee to an exchange when buying Bitcoin with fiat.
Bitcoin's deflationary design also makes it lousy as a currency, since why would you use it to buy two pizzas today when that same amount a few years from now might buy you a Tesla Model S?
Cryptocurrency probably does have a place in the future of commerce, but it will probably be something that addresses Bitcoin's serious shortcomings.