In a competitive market prices converge to marginal cost. In the case of transactions, this includes things like the cost of electricity to actually verify the transactions as valid, bandwidth, and the increased risk of orphans if you include more transactions in your block. It does not include the cost of performing proof-of-work. The only way miners who are "paid by transactions" are able get paid for performing proof-of-work is by overcharging by the transactions themselves, and they can only do this if they have some sort of market power. Thus it is impossible for mining to be competitive if proof-of-work is paid by transaction fees. It also results in further destructive incentives, as miners try to scoop up and horde transactions (for example using a sybil attack), since transactions are no longer competitively priced, but no represent a source of profit to be "mined."

There is also the free rider argument. If long-term-holders just hold and don't perform transactions (i.e. generate fees), miners won't do work, and the block chain won't be secure. The holders could do the mining themselves, but again only if they collude. Individually the incentive is for each holder to sit out and let the others holders pay the costs. The higher transactions fees go (to pay for proof of work, remember?), the greater the incentive to just sit on your coins and not pay them. This only reaches an equilibrium if some individual or group acquires all or most of the long-term holdings, so that individual or group can pay the mining costs without being exploited by free riders. Failing that, you have insufficient security, and likely such a coin will never become very successful (this includes bitcoin, although I think its possible now that bitcoin becomes a version of fiat).

So no structural mining reward means either extreme concentration of power, either in mining or holdings or both. One way to look at a structural reward is a consensus among the holders to share costs (since all holdings are being diluted by inflation) instead of relying on individual decisions to incur costs and suffer from a free rider problem.

Pricing remains an issue though, as no one has come up with a good model for how much mining should be performed, and how it should be paid for. "None" is clearly wrong though, in the proof-of-work model. Using proof-of-stake (if that can be made to actually work) or something else is another question.