The primary problem, as detailed in the article, is that homeowners have every incentive to be against new construction and no incentives to be for it. If property taxes rose appropriately with property values, homeowners would have an interest in maintaining housing prices rather than doing everything they can to keep them rising.
There's also a range of beneficial secondary effects. For example, I've talked to retired folks that have considered leaving the bay due to the increased cost of living. But because they have owned their house for decades + P13, if they bought a _cheaper_ house elsewhere in CA to downsize, they'd be paying _more_ in property taxes, to the point of the move not being worth the cost. (I believe there's been talk of transferable tax rates to fix this specific problem, or maybe something was even passed, but it just goes to show the distortions P13 has beyond the obvious).
Aligning incentives (where possible) is, imo, almost always a better way to do things than creating a new batch of regulations/laws to deal with a problem.