1031 exchange by itself only defers taxes (which can be helpful for cash flow purposes). People combine it with the stepped up basis loophole to avoid taxes completely.
As for Proposition 13/58 inheritance, note that Proposition 19 (2020) restricted the inheritance benefit to only family homes and farms, so I don’t think inheritance is a widespread benefit anymore. Proposition 19 also made the property tax basis portable, so the increasing property tax is no longer an impediment to grandma moving.
(AIUI,) You can't 1031 exchange an owner-occupied property into a rental property. (1031 is a "like kind" exchange treatment and you can't take personal-use property and directly 1031 into business-use property.)
In California - obviously prop 13 if someone in the family plans to keep the house.