That's not the parent's point. If I buy a $1M home in CA 10 years ago and I pay 1% in taxes then and the house is worth $2M 10 years later, I don't get charged

That's not the parent's point. If I buy a $1M home in CA 10 years ago and I pay 1% in taxes then and the house is worth $2M 10 years later, I don't get charged 1% of $2M after 10 years. I get charged a marginal increase ever year and this increase isn't based on market norms (I forget what the actual # is, but it would be like paying 1% of $1.25M). This means, if I sell my $2M house after 10 years), and buy another $2M house next door, my taxes are way higher in my second home due to prop 13.