"I ran some simulations, and if blocks take 20 seconds to propagate, a
network with a miner that has 30% of the hashing power will get 30.3% of the blocks."
Peter_R's analysis of fee markets in the absence of blocksize limits [1] shows that the hashrate advantage of a large miner is a side-effect of coinbase subsidization. As the block rewards get smaller, so will large miner advantages. An easy way to think about this is as follows:
Currently, the main critique of larger blocksizes is that we'll connected miners can cut out smaller miners by gratuitously filling up blocks with self-paying transactions. This only works because block subsidies exist. The moment block rewards become comparable to block TX fees, this exploit ceases to be functional.
Basically, large miners will still be forced to move full blocks, but it will go against their interest to fill them with spam since their main source of income is the fees themselves. As a result, large miners (unlike smaller ones) will lose the incentive to mine an un full block this evening the playing field.
In this context, large blocksizes as proposed by BIP100-101 hope to stimulate the increase of TX fees by augmenting the network's capacity. The sooner block rewards become comparable to block fees, the sooner we will get rid of mine centralization.
Dpinna