If, as you point out, the "market cap and average BTC per address directly affect how much wealth can be transacted through Bitcoin in any given period of time" then a low market cap or low average BTC per address will result in a lower limit on the amount that users are willing to spend on fees per transaction. As such, the only way miners would be able to increase their net income would be by increasing the maximum blocksize.
Assuming the market cap is in USD while transaction fees are in BTC, which miners then convert to fiat (taxes/electricity), discussing profits in USD seems appropriate.
Miners' profits should be dependent on a delicate equilibrium between a transaction publishing bottleneck decreasing Bitcoin's USD exchange rate and being able to demand higher fees, assuming people have a demand for transaction speeds. Any single miner controls a market share of potential transaction publication. Therefore any miner should be able to cause a percent increase in average tx fees as a function of USD by limiting the number of transactions published. Whether or not this sort of strategy can increase their overall profits is dependent on their market share and the demand for quick transactions at that particular time. I suspect quick tx demand shifts on a 24-hour scale. Just another reason to be concerned about concentrated mining pools.
An increase in nominal BTC profits would be very easy in this scheme, depending on market share.
Example: OPEC doesn't control all of the oil. They don't even control most of it. They still manipulate prices to increase their profits by limiting their supply.