Yes, cryptocurrencies do have value.
To be a medium of transfer of value, a cryptocurrency has to have value. This comes from the cost of acquisition. If a coin is Proof of Work, then a miner must spend money on hardware and operational costs for their mining setup in order to acquire coins. This way, coins are imparted with a value determined by the cost of production. A more rudimentary introduction of value can come from an ICO: if someone pays money for a coin, it is reasonable to think that they will not want to sell it at a loss. Any value which is introduced to a coin beyond these value formations comes from the price that someone is willing to pay to buy the coin. That price is informed by scarcity.