Earlier quoted context omitted.
You ignored the main detrimental effects of Prop 13 I described in my comment and addressed only the rent control aspect.
How did it tie the hands of the legislators?
Any new taxes, even revenue neutral ones, or increases in existing taxes require a 2/3 majority vote in both houses, which was essentially impossible until very recently. A consequence is that loss of revenue from one source could not be made up by taxing other sources. Conservatives even tried to argue that Cap and Trade was a new tax and was not allowed by Prop 13: http://legal-planet.org/2017/04/06/court-of-appeal-confirms-....
The only way to fund new programs was by ballot initiative, which requires a simple majority vote. Ballot initiatives don't pass unless all funds are earmarked for the specified program, even if revenues for the proposed tax or costs of the proposed program change over time. Ballot initiatives that issue bonds are even more likely to pass because they don't require an immediate tax increase. The result of a few decades of Prop 13 is California's ongoing budget problems with high taxes and poor allocation of revenues.