Would actively deciding what to save become something that ends up biasing future historical exploration to the point that it makes the enterprise dubious? The sites we have for study are completely random, and that definitely biases our view of the past. Think about the generations of people in the deccan who built and lived with perishable material that have no record beyond the impact they had on people who built with stone, or how we pay so much attention to a hundred year period of Roman history but can't figure out where Valerian was at certain crucial engagements because of the sources available. Would the process of saving sites not create a similar issue in the future?