Why would you trade any of the centers? Toews is getting older, and only has three years left. By the time the Hawks properly rebuild, his contract will be up. Even if he’s re-signed, he’ll be 35 and far from a viable 1C. Wouldn’t you rather have the flexibility to have some combination of Strome/Dach/Toews down the middle than trading the guy who will be in his prime in three seasons and is the surest thing of the three to be a top six center at that time? What if Dach doesn’t pan out as a top six center? You’ll be stuck with a 35 year old out of contract and on the decline and a guy who isn’t a top six C. Why would you throw away a top six center so easily?
Obviously there is a little gamble there, but Dach looked fantastic this season for us. I know some will disagree and say he wasn't ready, but I'm much more confident in Dach over the next decade then I am Strome. I liked how Dach looked more than Strome for most of this season.
You're right that in a few years, Toews will be a shell of his former self. However, the Hawks are likely drafting in the top 10 this draft (a draft that has a ton of centers in that area). And most of those players there would only need a season or two to start to jump to the NHL (even in a limited role on the 3rd line).
And more than that, I don't know that Strome is a guy who you compete with, especially if he's your best center. He's good at putting up points, but his defense is suspect and he's not much of a line driver.
I wouldn't mind him staying provided we have at minimum one center better than him at all times (outside of injuries), but I would certainly move him for a winger or defender of a similar value if the opportunity arose.