Those cities (though not in the ideal location for this project, I guess) would likely be ecstatic to have subsidized assistance (though who subsidizes it?). They're losing the beaches no matter what they do, the question is how long will it take, what will it cost to push it out a few more years, etc. For cities that don't have the budget to dump millions of dollars worth of sand only to have it mostly wash away in the next storm, a green beach is probably much more appealing than no beach.
Most of those beaches are in developing countries. If nourishing the beaches with olivine has some unforeseen, negative ecological consequence, those countries might not be financially equipped to deal with the cleanup. How are those beaches going to be insured?
In the case of California, I'm not familiar with their beach nourishing process, but I assume they are using sand that is more similar in content to what was naturally present. If the beaches have been replenished for years, then we at least have some idea about the short-term effects.
I don't know what the right answer is on this question, but I know that the pain of climate change will be felt by poor nations more than it will be felt by rich ones, no matter what. It may be that staving off climate change, even if it has its own negatives, is less bad than the alternative of doing nothing for those places and communities. But, maybe not. Hopefully it would get a lot of study and small scale experimentation before going big.