It's not about transferring value - it's about substituting currency-equivalent value. What's the substitution going on in a mining pool? (And don't say electricity for coin, electricity is not valued similarly to a currency. Similarly 'claim on mining output'.)
The currency equivalent value is securing the chain of BTC transactions and discovering new blocks, making the system work at all. New blocks have a currency equivalent value and doing transactions has a currency equivalent value too.
