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Today, it costs the entire network something like $0.001 to process each transaction.
The limiting factor is checking to see if the transaction is valid or not (the CPU cost of ECDSA signature verification). When the transaction volume gets high enough miners will have to start prioritizing which transactions they check, and they will use transaction fees as a quick initial check to see if they should invest CPU cycles to include transactions in a block. Yes, miners want to include as many transactions with fees as possible in their blocks, but it won't be economical for any miner or mining pool operator to include an infinite number of them.
And speaking of mining pools... they are a lot more efficient than individual miners because they allow transactions to be verified once instead of requiring that all of the miners in the pool do that work. Very small miners will be driven to join a mining pool, and the big mining pools will be competing to have the lowest fees and highest payouts (and so will be optimizing their ECDSA verification code and will figure out which transactions are profitable and which aren't).
So: I don't think bitcoin will have very few miners. I think it will have lots of miners connected to a smaller number of mining pools, and the whole system will optimize itself to be wonderfully efficient.