I know you can use your time out, obviously, it's just that most coaches don't. They use the time allotted before the next puck drop to challenge the call or not. This is what I meant by "spirit" as opposed to any written rule. I really don't have a problem with Torts here
You seemed to miss the question I ended with, which, as I've said above, gets to the point I was raising. Will this becomes a standard practice (call a timeout before challenging or not challenging)? If so, is that better for the game?
Well you gotta admit the way your OP sounded it seems like you are implying that using a time out is in some way cheating or unfair. However, most people have stopped by this thread already to point out various reasons why that is untrue.
As for the second part of your post, I think it could become a more popular move for coaches to make if they are not 100% certain that their challenge would succeed. It gives their video guy a little more time to analyze the play and inform the head coach. Team burns their time out for extra surety that they will not be penalized for a bad coach's challenge.
The time when you would not want to burn your time out first is when the play is obviously, egregiously wrong. We can all joke about "haha refs suck and are blind" but hugely missed calls like this don't happen in every game.
Also, there's no guarantee that an opportunity will come up later in the game for your team to need a time out, so that's another reason to use it here instead of waiting for a moment that might never come and not even using a time out.