You are ignoring the cost of the bitcoin network. Someone has to pay for all of those hashes. Currently it is being paid for by block rewards mainly to the miners, and the transaction fees are very low. Taking into account the bitcoins created to pay the miners, the cost per transaction is much higher with bitcoin than with traditional banking.
Nah, they're not linked. That is, if the entire planet had 0 transactions for the next 24 hours, you'd still award bitcoin miners the same block rewards every 10 minutes for the next 24 hours. In other words, block rewards are not a per-transaction cost, they're a systemic cost.
And that cost is dropping. Money supply is just inherent to bitcoin's design to kick it off, but it's dropping to near zero within a few decades, unlike systemic costs of printing fiat which remain endlessly.
The long-term reward are transaction fees, and those are certainly quite cheap. You can move millions of dollars with pennies of fees, or you can make one transaction with thousands of outputs, also for mere pennies. Those fees can stay low as when you get 1.000x more transactions, you can pay for the same security with extremely small fees per transaction. (i.e. securing the system is expensive, again it's a systemic cost, but securing each individual transaction isn't, that's just a cheap process of verifying a signature and storing 1/10th the amount of data of a tweet. So if you get enough transactions going, securing the system can be funded by very many very cheap transaction fees. And if you don't get many transactions going, then bitcoin isn't popular and well used anyway and who cares then if it doesn't work? It's like saying Myspace has technical flaws, nobody cares if it already failed to become popular that it would also have failed for technical reasons.
Bitcoin is imo unlikely to ever let you buy a cup of coffee using a single blockchain transaction (I mean, you can now, I'm talking sustaining this over the long term). Instead, it'll be used as the value network on which financial systems are built that will allow you to do this. Whether that's sidechains or offchains, they'll all use bitcoin's blockchain as a settling mechanism, without forcing low-value transactions on a permanent global ledger.
And you are ignoring a much bigger issue. For instance, the Fed has expanded the USD monetary base by about 4 trillion in the past six years. So why not take that figure, divide it by the total number of transactions in the past six years and call it "the dollar's cost per transaction"?
Every inflationary currency system suffers from the same problem. At least bitcoin has a hard cap on the total number of units that will ever be available.
There's not a ton of research but it's not really a difficult topic to get some superficial answers on cause it's all on the blockchain which is public of course.
For one we have the transaction numbers (again just count transactions on the blockchain) for the past 24 hours. It's been averaging about 100k the past few weeks. (averaging about 70k for 2014 for context).
We also know that every 10 minutes a block is mined and 25 bitcoins are rewarded with a value of $200 per coin. So in 24 hours that's $720k.
In short this puts the average supply of bitcoin at $7 per transaction.
In short, you can't call it a 'cost per transaction' because it's not a marginal cost. i.e. if zero transactions were made, there'd still be a supply of 25 bitcoins every 10 minutes up to $700k per day. Same with if 1 trillion transactions were made. In other words, this is simply a supply function, not a per-transaction cost function.
To put this into perspective, here's an example. e.g. if you build a bridge for $1m and you have 1 million users, the average cost per user is $1. But if only 1 person uses the bridge, it's not like the cost of a bridge is $1 million per user. That would be ridiculous. If we went about reasoning like that nobody would build a bridge at that cost, especially not in places where you get many users because you'd get insanely expensive bridges (1 million users costs 1 million * 1 million!)
Now it's true that someone has to pay for all this hashing which secures the blockchain. But that cost is not to secure each individual transaction. It's a cost to secure the system, a systemic cost. A bit like the cost to build a bridge, a global cost, not a marginal one (i.e. it doesn't cost extra to let 10 persons instead of 1 person to walk over the bridge)
The bridge is a poor example because you can't get unlimited people on the bridge. (there is some marginal cost, i.e. there is a cost difference to building a bridge to move 100 people per hour versus 100 thousand people per hour). In bitcoin this difference is trivial. It's like asking what the cost of a tweet is on twitter's bandwidth or storage, it's very tiny like a tiny fraction of a penny. This cost is paid for in transaction fees.
So to return to the systemic cost, you need to come up with enough money to incentivize miners to act honestly. And we can do that by rewarding them with bitcoin. Today that comes from block rewards, but it doesn't have to be like that. In 10 years, if bitcoin is popular, we can see millions of transactions per block, and if each transaction costs a penny then you can easily cover today's block rewards.
For some example numbers: current security costs about $5k per block, and we've just heard bitcoin's Chief Scientist report on tests that he did with large blocks. His tests showed he can power 200 megabyte blocks on his 2012 home PC. That's enough data for more than 400k transactions, meaning that with 0 block rewards you could get transactions as cheap as 1.2 cents, nothing close to the $7 figure I stated before.
And this ability grows at Moore's, Kryder's and Nielsen's law (cpu, storage, bandwidth) meaning that the ability to power larger blocks grows by 80x every decade or so. If you then fill those larger blocks with 80x transactions, then each transaction can get 80x cheaper. Within a decade we could get to fractions of a penny per transaction.
Then combine that with the fact that 1 transaction can carry a ton of data. i.e. you can send bitcoin to thousands of people with 1 transaction if you wanted. Or you could use bitcoin as a settling system for offchain or sidechain systems, meaning you can settle thousands of trades with only a few transactions making the cost of transactions even cheaper.
In short bitcoin really is very cheap and its cost will not be its downfall. It might fail for other reasons, but I don't perceive costs to be one of its obstacles, rather it's one of its competitive advantages.
