Suppose all the miners form a cartel. They will have no problem funding themselves; they can all agree not to include any tx that doesn't pay high fees. The users would pay this fee because they have no other choice.
Some users will try to pay a fee lower than the cartel's threshold. One miner decides to defect from the cartel; he includes in his block all these low-fee transactions. This costs him nothing, so this is a net profit for him (he benefits).
Seeing this, users will know that even if they don't pay the cartel's high fees, they can still get their tx included eventually. Thus, their willingness to pay high fees is lower (that is, the miner consumed their willingness). Thus, more users will try to pay low fees, and the total revenue of all miners decreases.
But it's not just the one miner. Every miner will, individually, have an incentive to include low-fee txs. This means that even with a low fee, it's easy to get a tx to the block. Thus, no user will want to pay high fees, and the total revenue of miners will be low (this is the tragedy - for the miners, and due to the effect on network health, for all Bitcoin users).
OK, I understand that explanation a bit better.
The key factor is that it doesnt cost any more to produce a block with the extra low fee paying transactions in as well than to just include the high fee transactions.
Even if the miners didnt collude to form a cartel I think that some form of natural cartel would form and the transaction fee would reflect the cost of mining.
There would be a certain percentage of miners that would try and include any low fee paying transactions in their blocks (and maybe the community miners too, who want to provide this service) but for anybody with a reasonable share of the total hashing power it would definitely be against their long term self interest to move too far away from a cartel price (whether the cartel was natural or not) and I think that miners with a large share of hashing power would act according to these long term interests.
The market for digital products is similar in that once you have built the software for a computer game it doesnt cost you any more no matter how many games you produce. However we dont see the market price being driven down to the actual costs of production and below even though there is a willingness to pay a lower price. Perhaps this isn't a perfect analogy either, but it has some similarities.
I tend to think that the market would still reach an equilibrium with the major miners sticking to a certain price level to protect their long term interests and the result would be the consumer choice of how quickly their transactions will be processed.
This is completely analogous to the classical instance of tragedy of the commons, where all herders would benefit if they all grazed just their fair share, but everyone is incentivized to defect and overgraze, depleting the resource and causing everyone to suffer.
I would probably still argue that there is a difference in the analogy that might make any insights gained potentially misleading. In your case it would be the suppliers of the resource that are cheating the system by defying the cartel and reducing the price of the resource, rather than the consumers that are over using and depleting a finite resource, but I agree that what we decide to call the problem isnt too important.
If we agree there is a problem (do we?)
There is definitely a potential problem. At the moment I wouldnt like to guess how it will develop or what is the best solution if/when the problem does appear.