I feel like the intuition behind prop 13 is similar to rent control but for land owners. Basically it freezes the price owners have to pay in taxes, so if the price of land goes up dramatically, people who have owned the land for longer pay far less in taxes.
For example, person A bought a house in SF 25 years ago for 300k. Person B buys an identical house today for 1.5M, therefore paying 5x as much in taxes every year even though both houses are worth the same value. This stifles development because any time land changes hands, the taxes dramatically increase. Even though you could make more money turning a parking lot into housing, people often don't because the taxes would increase to a point where it wouldn't be worth it.
The simplified end result for prop 13 (and rent control) is that young people are basically subsidizing old people through their taxes (and rents), keeping prices artificially high. It is incredibly hard to repeal these laws because most of the voters are unfairly benefiting from them or don't comprehend that rent control hurts them.
In the example I'm thinking of, it was a meeting about a law that was due to expire that limited new development to 5 stories, and effectively limited average height to 3-4 stories due to floor area ratios, and simultaneously put strict limits on the number of housing units you could build per acre. Mind you, this expiration would affect just the dense downtown core around the train station, not the vast majority of the city, which is zoned single family. They still hated the idea, it'd cause too much traffic. One lady gave an impassioned speech about how the drive to their second home in Tahoe, which used to take 4 hours now took 6-8 on Friday due to traffic. This came right after a speech from someone who was about to lose their primary residence due to rent spiking. I don't know how she was able bring herself to follow that, but she certainly tried.
First, a lot of property is opened up to the market because people are now willing to sell it, which should lower housing/land prices in general and enable more development. Second, the state gets a lot more tax money to use for education and whatever else.