It does increase the tax on the new property that the seller is acquiring, because for a given level of government spending, if the government gets less tax revenue from long-term owners they have to get more from newer owners.

It also increases the minimum price the seller is willing to accept for the property, because they won't sell unless the buyer offers enough to compensate them for the higher tax rate they'll have to pay on the new property. It increases the bid/ask spread on long-held properties, so that more often no transaction takes place at all until e.g. the owner dies and the property is sold in an estate sale for less than the owner would have been willing to accept if they were still alive.

I don't think you understand property ownership in CA. This is most definitely not what happens.

Also to add to this discussion is the various props and "tax treaties" between counties that allow old homeowners the ability to transfer tax basis from their old property to the new one they're buying. But this is a once or twice in a lifetime deal.

No actually prop13 limits both the property tax percentage of market value as well as increase of the tax from year to year.