First off, you don’t know what the proposed AAV was and neither does anyone here.
Second, I think you’re omitting some pretty critical information in your description of said 37 year old.
What do we know?
We know based on the reports that the Bruins had an offer of 2-years, and the Marchand camp wanted 3. Bruins came back to the table with a 3-year offer but the value wasn't what Marchand was looking for. Marchand even tried a face-to-face meeting to try and bridge the gap, but they still said no to his number.
We also know that less than a year ago, Sweeney handed out a 7-year deal to a player outside the organization value at 7.75 million per year. That player was a lesser player than Brad Marchand was then, and a lesser player than Brad Marchand is now.
We also know that his buddy Crosby faced a similar situation in Pittsburgh, and he didn't take a pay-cut on his new 2-year deal. Exact same AAV.
We also know the cap projections have come out since those deals were signed and it's going up over the next 3 years, a lot.
As a fan, I'm going to base my assumptions on Marchand's ask being
at minimum what he's making now and was likely higher than that. 7 million per. Maybe 8? From the time their first started negotiations on an extension, the bar has been raised IMO.
He shouldn't be expected to take a pay cut from what he's making now given his level of play this season. Why should he accept less than Elias Lindholm? Certainly, he shouldn't accept less just based on the fact he's older.
Meanwhile, I can see why management didn't want to hand out 6-7-8 million per for his age 37, 38, and 39 seasons. Considering this is a league with just two active forwards who are 39 (OV, Perry) and just two who are 38 (Malkin, Trevor Lewis) and just 5 who are 37 (Crosby, Nick Foligno, Giroux, Kopitar, and Zuccarello).
And they still did right by him, a player with minimal trade protection, and still took a lesser return to send him somewhere that he wanted to be. Keep him on the east coast. The team that has eliminated them from the playoffs the past two years no less. Hopefully that doesn't go unnoticed by future player acquisitions.
And who knows, maybe Marchand goes to market this summer and doesn't find what he's looking for. The door isn't permanently closed yet.