In a free market for transaction fees, spamming the network will have the effect of increasing transaction fees for everybody.
Maybe Mr Burns is more than just a common griefer. Maybe he is a miner with more rational motivations.
A miner has more to gain than to lose by spamming. Yes, eventually a spam equilibrium will be reached where the marginal amount you lose in your spam to the transaction fees of competing miners equals the marginal amount gained from your own transaction fees. But that is still a macroeconomically subobtimal situation.
To escape this http://en.wikipedia.org/wiki/Social_trap social trap, more than a market is needed.
Some simple but effective rules should be hardcoded into the Bitcion protocol/specification itself, to discourage the excesses of spamming.
I know that this approach probably sounds too “top-down” for the free market enthusiasts in this forum, but the rules should of course be purely voluntary and consensus based, like the 21M rule we have already.