Bitcoin transactions seem to have cheap fees, because everybody forgets that the block rewards currently act as subsidy to keep them low. On average, a transaction costs between $30 and $40 if you do take them in account, and thats way higher than most banks charge, and way too high for micro-transactions.
Now suppose that Bitcoin had no block rewards right now (like it will in the future), there can only be two possible outcomes: either that the hash-rate would drop to much lower levels, and the fees would stay the same. Or that the fees would rise to about $40 per transaction, and that the hash-rate would stay the same.
My gut feeling would say that even with a massive drop of hashrate, Bitcoin would still be secure, because the current hashrate seems like overkill to me. But in my previous topic (Alternative initial distribution of coins) various Bitcoin-veterans (like DeathAndTaxes) stated exactly the opposite: that Bitcoin wouldnt be able to survive if miners received just the fees and no additional rewards. So the expert opinion seems to be that the network would be unusable.
You missed a possible outcome.
Bitcoin could gain popularity, and the number of transactions per block could increase. Then the miners would receive increased total fees, without increasing the fee per transaction. If the current fee is approximately $0.06 per transaction, and a full block might have 4,200 transactions, the miners can already collect $252 per block. If we increased the maximum block size from 1 megabyte to 60 megabytes, then $0.06 per transaction would completely replace the 25 BTC per block subsidy.
More likely the fee will increase a bit, and the blocksize will increase a bit, that way we won't need to jump all the way to 60 megabytes per block. If we double the typical fee to $0.12, then we only need 30 megabyte blocks for the transaction fees to replace today's subsidy.
The other alternative (higher fees) also seem to make the network unusable, except for high-value transactions, which are a minority.
If the maximum blocksize is not increased, then this is a VERY likely outcome. At that point, bitcoin would most likely become a sort of clearinghouse for some other payment type.
So if both are true, is it safe to say that block rewards are just a subsidy for Bitcoin's ridiculously high transaction costs?
Yes, the block subsidy is just a subsidy for transaction costs. By way of inflationary effects, the entire network is splitting the current costs of mining. You could even look at it as a "tax" that every owner of bitcoin has to pay in reduced value for the bitcoins he holds to pay for the existence of distributed consensus.