What do I mean? Well, let's take the Teriton Apartments on San Vicente. The City's historic resources consultant did a lengthy review of the building, and said it met NONE of the requirements for designation as a landmark. The tenants said that 1. It was at the end of the block, 2. Some people who later became famous stayed there, 3. It is just like lots of other apartment buildings built at the time, 4. We know the architect's name, and 5. It's been there a while.
Moral of the story for future landlords: redevelop frequently. Blow up the buildings before the City can decide it's a landmark, or you have forfeited any right to change the use of the lot, modernize it, or expand it.