Barriers to movement causes an inefficient use of housing with respect to commutes and job sites. Someone locked in to a house in Mountain View with a job in SF cannot trade houses with someone locked in to a house in SF with a job in Mountain View - not without a huge increase in property taxes.

The redistribution gets rid of a deadweight loss in commuting, easing traffic and transit congestion and allowing more housing to be within commuting distance of jobs.

Sure, but that is just a symptom of the overall problem. We aren't going to get anywhere by just treating the symptoms while ignoring the cause of the problem that there are more people than there are places for them to live.

Repealing Prop 13 also removes another impediment to increasing housing stock. People who already own property and don't feel the effects of quickly increasing property prices will vote against new development more often than people who have to pay higher taxes when property values go up.

That argument relies on somewhat circular logic. You say one cause is that home owners don't want new housing. You solve that by repealing prop 13 giving them a financial stake in the market value of homes. However, why would the home owners support that repeal if they are against new housing in the first place? Either the home owners are against new housing or they aren't. If your suggestion was a feasible solution to the problem, it would prove that that your proposed cause was not actually the cause of the problem.

You missed the argument. The argument wasn't that homeowners should support repealing Prop 13 because it creates more housing. The lower taxes alone are enough to keep them from wanting to repeal it. The argument was that everybody else should support repealing Prop 13 because it gives homeowners one less reason to support more housing. There's nothing circular about it.