I think the reason miners are not taking advantage of ways to increase transaction fees is that the transaction fees are miniscule compared to the block subsidies at the moment. It will be more relevant in future, or would be now if more people voluntarily pay very high transaction fees. But I don't think that's a good position to be in.
This is all as-far-as-I-know, please correct me if I'm wrong. But -
The thing that bothers me in the longer term is that miners have absolutely no incentive to include a zero-fee transaction in the block, whether it's so-called "high priority" or not. Even in the short term, because the subsidy outweighs the transaction fees by a significant margin, you might as well just never include any transactions in your blocks. Not healthy for the network! I noticed a block the other day which was the first one for about half an hour, and it only included six transactions. That is not useful miner behaviour.
Is it not possible to offset the proof-of-work requirement by some metric involving number of transactions in the block and/or volume of transactions, so that miners have an incentive to do useful mining instead of just hoarding the subsidy? Or is that too open to abuse?