Let's put it this way. If a new employer asked me to show photos on my phone, I'd flat-out refuse, and would be highly suspicious of him/her going forward. It strikes me as bizarre.
As we all know, there is a very high level of conformity in the hockey world, especially among younger players. If you're a 18-20 year old non-star player, and one of the most famous coaches in the world asks you to do something you're uncomfortable with, you're likely to do it regardless. There's a huge power imbalance at play - none of these guys are going to tell Babs to get stuffed.
I'd object on principle, even if I had nothing to hide, but these young players could have pictures of themselves partying, indiscreet photos of GF, or maybe even evidence of being in the closet. And then consider Babcock's rep for trustworthiness, ie the Marner story. What's on a player's phone is none of Babcock's business.