(I wish there was a meta.n.y.c where we could discuss things like this. Alas.)
When you think about it that way, they almost all look pretty ridiculous. Should the San Francisco city charter have an amendment about whether one particular construction project in 2014 can be built at a certain height? Should we have a ballot initiative every time a new building needs to be built?
That might make sense in some alternate reality if we lived in a direct democracy with routine voting and people actually informed themselves about the issues they were deciding. I think it's pretty safe to say that we aren't living in that world today.
Instead of capping the tax, we should cap the amount of the tax that actually has to be paid in a year in which the property does not change hands. That number could be limited according to the Prop. 13 formula; the city or county would receive a lien for the difference, that lien not becoming due until the property does change hands.
This wouldn't change anyone's cash flow until the property is sold, at which time the city or county would receive the unpaid amount out of the sale. The unpaid amount will be a fraction of the amount by which the property appreciated (or if its value fell, the unpaid amount will be zero), so this will be relatively painless.
I've read that this has been done somewhere, though I don't recall where. It's clearly possible. No one is forced to sell, and the localities still get their tax money.
Consider that the standard commission paid to the listing agent when you sell a property is 6% of the sale price, and you'll see that these amounts are not significant disincentives to selling.