Regarding the HCM designation, an owner is not prevented from demolishing or renovating the home, however, any demolition or substantial renovation has to be approved by the HCM board. If you don't get approval from the board, they can delay a demolition or substantial renovation by up to one year, but they cannot stop it.
And this doesn't take into account any other sort of zoning that might affect the property, such as limitations on square footage, etc.
So, ultimately, whoever buys this could tear it down and build a cookie cutter monstrosity (honestly, this isn't a bad price for LA), but they'd have to hold on to it for a year.