I was probably still not clear enough. Bitcoin is inherently expensive because the security of the system is based on burning money, all the cryptography is just kind of an implementation detail. You could as well place a ledger on a table next to a camp fire and everyone can come to the fire, throw some bank notes into it and this allows him to fill a page in the ledger. Same thing. And it really makes no economic sense because the money is totally wasted. I don't doubt that there may be a successful cryptocurrency one day, but it will not be based on proof of work.

When you think about it closely mining is just a way to establish identity in an anonymous system. You want to reach consensus on which transactions should go into the next block and which not, but because you also want anonymity you can not just ask everyone for a vote because nothing prevents the bad guy from having a billion false identities all voting for his bad intention. And here mining comes into play, it makes voting expensive and prevents you from casting a lot of votes. Hundreds of millions every year just to agree on which transactions to include in the block chain. It does not even help in any way to protect transactions because they are entirely protected by public key cryptography.

Had Bitcoin a central authority you could for example just require everyone to send a copy of their ID in exchange for some cryptographic key that would give you one vote. Then you could just propose blocks of transactions and let everyone cast a vote and the winning block gets added to the block chain. No mining required and transactions become extremely cheap, at least if you manage to build an efficient central ID checking authority.

This is of course pretty unlikely to happen because it is against some of the core ideas of Bitcoins but any cryptocurrency that can avoid mining will have a huge economical advantage over Bitcoin and any other proof of work based system and will eventually replace them. Proof of stake is one idea but with its own problems. I think it is most likely that the winning solution has not yet been invented.

I digress. Okay, Bitcoin is expensive by design because the security is proportional to the amount of money burned in mining. The number of processed transactions is not directly coupled to the mining costs and therefore the costs per transaction can go down when processing more transactions but they are not completely independent either. A larger transaction volume requires more security which in turn requires higher mining costs. Processing transactions worth a billion every day with mining costs of a million per year surly would be a pretty dumb idea.

It is of course a tough question to figure out how high the mining costs should be. Easier question, how would I attack Bitcoin. Assuming Bitcoin became mainstream and used as much as PayPal or even credit cards and I just want to cause havoc I would probably go for a DoS attack. Obtain the required hashing power and just fork the block chain again and again. I didn't really think this through but just creating legitimate blocks with legitimate transactions but burying them in short side chain after short side chain so that they never get confirmed would be one of my first ideas. Probably way harder to mitigate then detecting blocks with few or useless transactions.

Do this for a couple of days and people will only want to get their money out as quick as possible. The Bitcoin price will crash in no time and people will lose a lot of money. Maybe you could even recapture some of your expenses by blackmailing people or betting on falling Bitcoin prices. But there are probably way more clever ideas then I can come up with ad hoc. Anyway, if mining costs are not high enough or in heavy disproportion to the transaction volume they protect bad things might happen. Back in the days of the cold war spending a billion Dollars on mining hardware to disrupt the Bitcoin based economy of the enemy would have been a real bargain.