TL;DR People in California are shit, California's laws are shit and the state is the poster child for why single party super-majority control over a legislature for extended periods of time is a fucking awful idea.
Prop 13 really isn't that big an issue in the grand scheme of things. The biggest issue is that there is a
massive 3.5 million housing unit shortfall in California. This shortfall is stems from two primary factors. The first is that there is a deeply ingrained NIMBY attitude that is endemic to California's populace and local governments. In my experience at least, Californians tend to be much more aggressive in resisting the construction of affordable housing than elsewhere in the United States. Sure, everyone wants those poor people and working class families to have housing but; they don't want it anywhere where they might happen to accidentally see any of the people that would live in those communities. Additionally, local governments will generally ignore California laws which require them to submit, and follow through on, long term housing development plans. Strangely too, Californians seem to have an aversion to building upwards (e.g. multistory apartment buildings.)
The second factor is California's regulatory bloat and legislative incompetence. At the state level, California's regulatory burden is already extremely cumbersome and is uniformly unfriendly to anyone looking to build housing in the state. Indeed,
state law ends up, on average, increasing the cost of housing by $22,000 compared to $6000 nationally. However, compounding issue, local governments also will impose heavy reporting burdens, capriciously levee steep impact fees, make the permitting process long and complicated as humanly possible, reserve the right to veto a development as "not fitting in with the established community or aesthetic" later in the building process etc. The regulatory assfucking to developers in California receive ensure that the cost of housing is driven up. As an added bonus, the restrictions also mean that any development will proceed at a snail's pace, which will further increase the front end expenses to builders which will, inevitably be passed on to buyers and/or renters. Additionally, the legislature's (I'm going to be generous and ascribe incompetence to their motivations, rather than corruption,) asinine response has been to throw money at the problem, in the form of state subsided housing. Oh, and any of these subsided construction contracts must be done by union workers at prevailing wage. This is fucking retarded I'd say that its only treating the symptoms of the problem, rather than the source (see: local governments being cunts,) but it doesn't even do that much, as the local governments fight tooth and nail against these projects. Which, wouldn't you know it, happens to drive up the cost of building the housing and makes attempts to build the housing extremely unattractive.