Check with your legal and tax counsels and I am not familiar with CA laws but so have a few DE and other LLCs, so here is my take:
1. Asset Protection - Depends on the states you own the property. Not sure there is much more protection it would offer.
2. Anonymity - Possibility. You can achieve the same and perhaps more by placing the properties in a Trust.
3. Tax advantages - For single member LLC, there should not be much if any difference as they will be treated as a pass through entity.
There will be a more paperwork to file and more fees (annual "shareholder tax", registered agent fee, etc)
If it is a multi-member LLC, then you will also need to create K1s.
Also keep in mind that most banks that issue Fannie/Freddie backed loans will not lend to LLCs (expect for delayed financing)
One area I do find some value in my LLCs is to give a more professional "business appearance" (for listings, collecting rent, etc) but I suppose you can also achieve that via a d/b/a a.k.a "fictitious" business name filing