I think the main reason they shouldn't, is because they would be wasting their time. The Red Wings would most likely have to offer him a salary over $10M/year to compete with other interested teams and to entice him to want to leave a team it sounds like he is very happy to be a part of.
Plus, Bergevin has already stated that he would likely match any offer sheet that comes PK's way.
IF the Wings were somehow able to sign Subban to an offer sheet and have Montreal not match, they'd have to cough up four 1st rounders. That would likely do more longterm harm than good. The Red Wings two "elite" forwards are on the wrong side of their prime, and it's getting harder in todays league to replace players like that through Free Agency and trades. Missing four chances to grab a couple of potential "elite" forwards, would make it that much more difficult to replace them.