I'm not in a first responder position, thankfully, where I need to make decisions between life and death for people but I presume that in situations like this LE has to take into account what is the least risk of harm to the greatest number of people. So for example, if someone is missing overnight and it is not known whether or not they are out in the elements (as was the case here), LE also has to consider how many others may be harmed searching and then make a decision. There have been plenty of missing children cases, some children much younger than this, where the official search was suspended for similar reasons. In the Delphi case, I think we've been told that finding them in the overnight hours would not have made a difference in terms of their survival. Obviously, LE didn't know at that time they were dealing with murder or even if the girls were still in the vicinity of the trails. LE didn't prevent people from staying to search if they wanted to - and people did stay, including volunteer fire fighters.
I don't know whether LE made the "right" decision in this case but I don't think that it materially affected the outcome as IMO the girls were already dead by the time the search started. As far as murders go, the bodies were found in a challenging scene from a forensics standpoint (outdoors) but were found relatively quickly, all things considered. I can't pinpoint this specifically and say the delay finding the bodies is why the crime isn't solved.