But shouldn't it be the case that if police is given a search warrant, we (as people, in general) want them to notice anything and everything there is to notice?

This is also something I would reply to your sibling comment as well, I think many would prefer a footage of their state instead of a description of it from a police officer who might be confused/distracted/filling-up-the-gaps. It is both more objective and more just. Jury should be allowed to see as it was and not just as it is displayed during the trial.