To answer your question, limited block space DOES NOT create a market for transaction fees TODAY; But there are still some fees because of the rules clients impose on relayed transactions. However, when the average transaction volume regularly exceeds the space available in a block (i.e. we always reach the maximum block size), this will create a market for transaction fees.
Miners can choose and prioritize processing based on fees paid. They don't today, for the same reason you brought up - block subsidy is still high - but they will in the future. Doesn't this create a market for fees, without limiting the network processing power to the ridiculous ~7 tps?