You are far more patient than me, I got annoyed with it when they first put Laine in the 2nd and it wasn't working at all. That was the end half of 16-17 and I have been wondering about it since. Because it defies logic. I think especially in the Vegas series they should have put all the eggs in one basket since they were lacking goals. Yeah, he is only 20 and plenty of time to destroy the league, but there's a possibility that they missed out on the cup last season because they had no backup plan for Vegas series where I would have certainly played Laine more minutes. Lacking goals, play best goal scorer more. Simple stuff.
Of course he has missed some personal hardware in the process (calder, rocket or two), and that might affect his motivation to sign team friendly. That's just my speculation.