That's fair. But it's only a big concern if you get fixated on adding a SPECIFIC player. ("Must trade for this guy.") Your options open up a whole lot more if you're looking at any of 7-8 candidates for a depth defensive defensemen who PK, rather than just the top 1-2 players for the role.
Even if half the league suddenly won't answer your calls, you're still looking at around a dozen players who fit the bill on paper. Then you can still get 11 rejections as long as you get one team who says yes.
A similar approach also applies to adding a forward, although the percentages obviously change based on scarcity. But if Yzerman is calling everybody about everybody, as if he wants to make TEN trades this summer, then he absolutely can afford to strike out 80-90 percent of the time and still come away successful. That's the level of determination and thorough use of available resources I want to see, instead of, "Well, we just aren't ready yet. We have to be patient." (As if one more draft pick in 2027 is the missing piece to turn it all around.)