A fun fact is that Bergeron never centered a shut-down line for Canada in best-on-best competition.
In 2010 he started the tournament on Crosby's right side, and ended up due to injury/poor performance as the 13th forward in a PK/faceoff specialist role.
In 2014 he started in a 4th line centre role (not in a shutdown role...that was Toews' responsibility), then quickly moved up to Crosby's right side and played there the rest of the tournament.
In 2016 he played the entire tournament on Crosby's right side.
To play a shutdown centre role for Team Canada at the best-on-best level, you not only need to be capable defensively, but you need to be capable of playing top-6 minutes against the best competition AND be capable enough offensively to earn those minutes, keep your opponents honest from a defensive perspective, and produce offensively. I thought the Toews lines in both 2010 and 2014 were our best lines in those tournaments for those reasons, as the were able to match up effectively against the opponent's top line, wore them down physically, and produced offensively (including scoring timely goals).
All to say, I'd much prefer someone like Point in a shutdown centre role than, say, Gourde or Danault, as Point is a significantly better offensive player and you wouldn't lose anything with him playing top-6 minutes. Gourde and Danault aren't good enough offensively to give those minutes to, we'd be giving up too much valuable ice time.