And the more expensive homes will also be an income tap when you retire and sell the house (hint: anyone in the magenta can retire, sell and live out their lives anywhere in the green).
So if you pay X in state income taxes, you'd deduct X from your overall federally taxed income. You end up only saving your federal tax rate times X, not X in federal taxes. So if you're taxed at 13% state and 35% federally, you'd pay 13% to the state. Then you'd still pay (barring other deductions) your federal taxes on 87% of your income.
Federal taxes don't work as a bare percentage, though. You pay a lower percentage on everything up to some number, then progressively higher percentages on brackets of your income up to your maximum tax rate. https://taxfoundation.org/2017-tax-brackets/
Compared with most other states, California has lower property tax rate. Since Prop 13 passed in the 70s, the tax rate has been fixed at 1% of assessed value (with maximum yearly increments on the assessed value capped at 2%).