The NHL has a hard cap. And unlike the NFL, you can't move cap money forward.
So teams have to be wary with contracts, especially big contracts (you can bury $1.25M in the AHL, like the Flyers are currently doing with Peterson).
And age curves apply to hockey like any other sport.
Hockey is a team game, that is, no one or two FAs will make you a SC contender, look at NJ, (2) #1 picks, a bunch of other 1st rd picks, they get impatient, sign Hamilton, trade (1st & 2nd) for Meier, sign Palat, trade Zacha for Haula, trade (1st) for Markstrom, sign Noesen, Tatar, Pesce, Dillon.. Result? They're 16th in point % and headed for a 1st rd exit.
Meanwhile, Caps sign Strome to below market deal, trade a veteran goalie for Dubois, trade 3rd and Jensen for Chychrun, pick up Sandin in a salary dump, trade (2) 3rd rd picks for Thompson (G), Protas (#91) becomes top scorer, McMichael (#25) makes big jump. Top regular season record. Bunch of smart, incremental value moves, no throwing money at "name" FAs.
Sign a 29 year old FA to a 7 year deal and you might get 4 years where he produces at the contract level, and 3 years of subpar performance on the back end.
You're actually better off signing an over 30 FA to a 3 year deal where he's more likely to produce over the length of the contract (lower salary, short-term). Where you have to hope the 29 year old is still productive at 33, you know the 32 year old FA is still productive (or you wouldn't sign him).