You and many others just don't understand the logic of the bridge contract (as a concept, not specifically the cheapskate one MB forced on PK).
The CBA does not give the players UFA status until 7 pro seasons, by and large. Until then, they are restricted, which greatly reduces their leverage because teams wishing to acquire them must also give up other assets, thus reducing the salary they might offer.
Furthermore, the very first contract after the Entry-Level Contract (ELC) comes without arbitration rights. Only an offer sheet can give the player any leverage, and as I said above, offer sheets come with dampened salaries due to the draft picks a team will have to give up to get the player, as opposed to getting an unrestricted free agent who can be signed free and clear.
In economic terms, the producer's surplus belongs to the team with RFAs, except to the extent an arbitrator might rule otherwise. However, the arbitrators are bound to use as comparables only other RFAs, so the system is pretty tight, and in the teams' favour until 7 accrued seasons (or age 27). An RFA can try to hold out, but even one who was as promising as Subban did not gain money from holding out, because the club's leverage trumped his.
A "bridge contract" is specifically designed to cover RFA years only, so that the club can get another contract negotiation with the player BEFORE he is an UNRESTRICTED free agent. So, for example, in the situation this year with PK Subban, while the UFA years loomed in the horizon and affected the negotiations regarding the later years of the deal, it was still a "monopsony" situation. In practice, only the Habs could effectively negotiate with PK; even if another team wanted to give him a contract, they would have to pay off the Habs first. Plus the Habs could match the offer, further discouraging teams from even trying this route.
Compare this with the frenzied situation that would occur if all 30 teams could negotiate with Don Meehan and PK Subban. Look at the overpayments often made on July 1st each year. Look at how guys like Scott Gomez and Wade Redden and Brad Richards and Brooks Orpik and many other non-superstars made out on July 1st, and imagine having that frenzy feeding into Don Meehan's office working their best for PK. Look at what Brad Richards got!!! Dallas liked Richards but could not hold on to him in the face of the unbelievable offers being thrown about. Now imagine if Bergevin had listened to those who said to give PK 5 years at around $5.5M two years ago. Picture the competitive pressure on Bergevin with Subban being a free agent at age 28 instead of age 33, which is when the new deal will expire. The inevitable result would have been either losing Subban, as he would be wooed by up to 30 clubs, or paying much more to hold onto him and hear him say that he always wanted to stay here.
That is where the short bridge contract reveals its worth. It keeps the situation cleaner with your 25-year-old restricted free agent.
Of course, clubs don't want to say publicly that the CBA allows them to take advantage of players under 27. So they make nice-sounding statements about how the player "has to prove himself", but it is BS. The Subban case reveals the BS, since he had already proved himself, but the club had to fib and many fans bought the fib, thus coming to the conclusion that MB was disrespecting PK.
PK said openly that he never felt that way. Don Meehan is a top agent and he was able to explain the business aspects to a smart guy like PK.
Too bad a lot of the fans can't benefit from having Don Meehan explaining things to them.