I doubt that other cities will copycat this bit of Berserkeley insanity (BTW, the "Berserkeley" nickname has been in circulation in central California for at least 60 years that I know of, so the City of Berkeley is not held in high esteem). Berserkeley would be a large-ish city in some states, but in California, ~120K is a small city.
If this passes (the provisions of Proposition 13 may make that difficult), at least some building owners will stop paying taxes and dare Berserkeley to take over the buildings. Depending on the proposed tax's particulars, this could result in a noticeable decrease in the supply of housing in the city.