The free market provides a solution. When the block size fills up, people will pay higher transaction fees to get their transactions through. Free riders paying zero or low transaction fees won't get their transactions processed.
The block size can only be increased if the big miners agree, and it's not in their interest to increase it.
I think it is in their interest. The value of bitcoin is hobbled by the small number of people who can use it, and network capacity is a major bottleneck. To boost the price of bitcoin there will need to be a large increase in the number of people holding bitcoin, and a corresponding increase in the number of transactions. That means an increase in the block size.