Beagle's role was to be a defensive 4th line center. It's the role he fulfilled in Washington and it is the role he has now in Vancouver.
His last two years in Washington, including the season the Caps won the Cup, he averaged 13:38 and then 12:27 time on ice per game. This season he's averaging 12:38. In his last two seasons in Washington is OZ start percentages were, respectively, 31.1% and 25.2%. This season it is 32.5%.
His useage this season is what it was in Washington. He's playing essentially the same role. He's not doing it as well, but then a player performing worse at the age of 34 than he did at the ages of 31 and 32 isn't exactly surprising.
Paying him for four seasons in his mid-thirties at $3 million per didn't make sense for the Captitals, so they didn't do it. It made even less sense for Vancouver, which signed him anyway. His linemates likely aren't as good now as the 4th line of the Caps was, he's older than he was and probably worse for it, but he's filling the role he was intended to fill, pretty much the same role as he played with the Caps and despite the thinking of the Canucks' management group, he'll never be worth $3 million per season to do it.