There _must_ be competition for block space to make fees a viable way to pay for security.
Limiting block space isn't the only way to increase mining fees. Removing/reducing the block reward has the same effect. Once the reward is less than the cost to mine, most miners will require a tx fee. Given this incentive, there's really no reason to limit the block size. It is in the miners best interest to set the limit as high as possible so they can receive the maximum amount of tx fees possible. For this reason alone I foresee the block limit rising significantly.
It doesn't really work this way. It costs nothing to include a transaction so a small, self-interested miner will include every fee-paying transaction, even a small fee. In so doing, he sells out the bargaining power of miners; users will see that low-fee txs are included, and will pay less fees in the future. The damage thus done is shared by all miners, but the profit from including the transaction is all his own. This is a
tragedy of the commons problem. The common resource here is the bargaining power of miners, which the individual miner will consume at others' expense.
This will be alleviated if mining is highly centralized (which we don't want), or if there are other factors such as assurance contract funding or a limit on total bitcoins transferred per block.