There is nothing requiring you to move into a property with higher taxes - you could substantially downsize or leave the state entirely.
Even if your costs and mortgage become more expensive, the tax system is still there to benefit you. The tax system will always reward home ownership. By time you are on your third house you will be paying cash, so even mortgage issues will go away. I don't know anyone on their third property who has a huge mortgage...maybe a small supplemental one but that is about it.
Not sure what the "barriers" to selling are...a good realtor will cover those details for you and in most parts of California, your house will sell very quickly, my last sale was less than ten days, about the same amount of time most renters probably spend looking for a new place.
Past performance is no guarantee of future results. Housing prices have risen faster than inflation in California over virtually any period ending today other than cherry picking the top of the housing bubble. Nothing says this will always be the case. Just ask the homeowners in Japan or in parts of the rust belt. I'm a homeowner in California but I also remember the last time everyone said housing prices only go up.
Furthermore, the tax system may not always reward home ownership. New caps on mortgage interest deductions are already affecting California houses although the effect is currently small. It used to be true that homeowners always itemized deductions. For 2018, it'll be about a wash for me as opposed to taking the standard.
And yes, the tax system will always reward home ownership.
Alameda, Los Angeles, Orange, San Diego, San Mateo, Santa Clara, and Ventura counties all allow this.
Persons over age 55 or who are severely and permanently disabled may transfer the base-year value of a residence to a replacement dwelling in the same county, or in another county if the board of supervisors of that county adopts an ordinance granting base-year-value relief to replacement dwellings when the original dwelling was located in another county
2. The cost of housing has risen significantly, compared to what you bought at. To sell your current house and buy an 'upgrade' would increase your mortgage bill, even if you dump the gain into the next house.
3. The higher barriers to moving since you have to list, sell, etc. While a renter can send an email and get a new place without much hassle. A renter can never be 'underwater'.