By far the most efficient mechanism humanity has ever come up with for distributing scarce resources (such as room on freeways) are free markets. The article is 100% correct that pervasive tolls are the only effective and fair way to reduce what has become monumentally oppressive traffic congestion in LA.
Tolls are a monopoly granted by the government, which makes it the opposite of a free market. The real result of a free market would be private roads or highways that would compete against each other for tolls. Neither are a great solution. Simply throwing more public transportation at the problem isn't going to help either.
If LA wants to improve their traffic problem, they need to address the root cause: bad urban planning and zoning laws. Where people work and where people live are in completely different areas of the city, requiring you to commute. They need to make local traffic easier (ie: not force you onto the freeway) and they need to reduce the need to drive all over the city every single day.
People will use free highways until they're at capacity. Throwing more public transportation at the problem does increase the number of people that can travel down the freeway, but it won't reduce traffic because any car taken off the highway by a driver switching to public transit will be replaced by another driver taking up the commute.