And you would be WRONG.
How in the hell is it good strategy to throw an offensive guy out there if we win the draw but not a defensive one if we don't.
Because putting a more defensive player out won't make much of a difference in preventing a goal at 3 on 3...
3 on 3 is too chaotic and there's too much space for skilled players to operate.
Julien/Ducharme literally already tried the tactic of matching strong defensive players against the top offensive players in overtime, which is pretty similar to what you are asking, and it failed miserably.
Every team has the same strategy and plan in OT. Keep the puck wear the opposition down. We lost that game without touching the puck.
The guys on the ice were not suited for that role of chaser.
Wearing the opposition down is not the main overtime strategy. Detroit wasn't playing keep away for a whole minute before scoring. They had 3 scoring chances before one finally went it.
When the opposition shoots, there's a higher chance the defending team gets the puck back than the attacking team. In this instance, Detroit managed to recover the puck each time they had a scoring chance, but teams are usually not that fortunate.
Our current strategy is to use someone other than Suzuki to try and win the initial draw if we win it he comes on to replace the center. What I'm saying is if we lose it he should not be getting on spending his energy chasing the puck. We have other players better suited for that. Dvorak stays on and the winger changes for Evans. Try and get the puck back before using your best offensive elements. I'm not saying it's going to work all the time I'm saying its better to have your puck retrievers on when you have to retrieve the puck.
You're acting like 3 on 3 overtime is the same as a powerplay where a team stays in the offensive for a full minute while the other team just defends. That happens, but it's not the general case. Overtime usually has a ton of back and forth with teams trading scoring chances.
As I wrote in a previous post, there are a ton of odd-man scoring chances at 3 on 3. Those odd-man scoring chances almost always happen after a turnover or scoring chance from the opposite team. There's no time to make a player change when that happens. So with your proposal, the habs would be more likely to have Dvorak-Evans on the ice for a 2 on 1 than Suzuki-Caufield, which is not a good tactic obviously.
I'm not even sure what your point is questioning the logic. If you have a sounder strategy I'd sure like to hear it.
Why would the habs need a different strategy than what they are currently already doing? They are 4-1 at 3 on 3 overtime this season.