Proposition 13 was designed to help people save their homes because taxes were out of control! Now that we have a state lottery, "they" have no excuses for poor schools, etc., so now they yell, "unfair!"
Proposition 13 was designed to help young couples and old people keep their homes. Old people do not sell and move from house to house and many young couples with children do not like to move and take their children out of school and away from friends.
Your contention that the stay-puts are making it hard for others to buy a home is a joke. Do you really believe that raising the taxes of the stay-puts will lower taxes for others?
Please don't underestimate the general public. We are very aware of bureaucrats who cannot stand not having unlimited taxes to spend.