If people knowledgeable about architectural preservation think something is worth preserving it is usually worth preserving. It is a question about knowledge, not taste.
Sometimes there is another interest that weighs stronger than preservation and something worth preserving must be torn down. Replacing a single family home with another single family home is usually not one of those.
With a extremely shallow understanding about the architecture of the US south west I find that building interesting. Shame about someone gutting in though. And there is also the fact that demolition should be avoided because of the waste of embodied energy.