I don't agree that it is in the miners best interest to have big blocks allowing for more transactions. The argument is that more transactions means more fees,

I don't agree that it is in the miners best interest to have big blocks allowing for more transactions. The argument is that more transactions means more fees, but that is not really the case. With a block limit just a little under what there is demand for, transaction fees will grow significantly for those that need to compete to be included in the next block. If the block limit is above demand, then there is space for any transaction and so every transaction just has to pay some symbolic minimum fee. The sum of this will be lower than the sum of fewer transactions but with higher paying fees.