And if the SAR team started an air search and no only lost the bird due to weather, but also the crew, people would be saying "they should have waited."

And they'd be right. Last time I looked, the thing you don't want to do when you are responding to a problem is make it worse. It might not be the pretty or popular answer, or the one that a lot of people will go with willingly, but there is a reason for it.