> One of the hugely compelling benefits of cryptocurrencies is they entirely eliminate the necessity for such middlemen taking a cut and driving up costs for the parties actually partaking in the transaction.

Without more efficient means of off-chain transactions (such as payment channels) the cost of on-chain cryptocurrency transactions is typically much more expensive than credit card transactions (except for very large amounts, as credit card transactions charge a percentage, and cryptocurrency transactions have a fee not related to the amount transacted).

For some of the cryptocurrencies those fees are currently somewhat hidden, as you don't directly pay them as transaction fees, but as miners get a block reward that contributes to inflation. If you include the miner revenue a Bitcoin transactions currently costs about $20 in average: https://blockchain.info/charts/cost-per-transaction