Babcock trapping with the lineup he had when he first came here makes sense, you're not going to run PA Parenteau head to head against Crosby and hope to win 5-4.
But again, that's an example of a bad team running a trap because they have no other choice. Forcing a low-event game increases the chances that a bad bounce or deflection results in the game deciding goal. That's a good way to improve your odds of getting to OT against a good team, but that doesn't really work when OT points no longer matter in the playoffs.
The trap also doesn't have a way to deal with forwards who are bigger, faster, and more skilled than you cycling for full shifts at a time. Sure, it reduces how often those cycles happen, but they're still going to happen. Now, the refs may decide to look the other way on hooking holding and interference against the cycle, but that's not something Columbus can control.
To me, it comes down to whether or not Columbus can hold on long enough to let us beat ourselves, I don't see a situation where they're actually dictating the pace of play and in control of the game.