It would have been hard for Yzerman to get the team any better any faster with what he was left.
That being said, I'm starting to feel a lot of concern for this off-season and beyond. At some point you have to start actually targeting marquee free agents and making actual hockey trades. A half season of Patrick Kane showcasing himself for his next contract is fun, but eventually Yzerman is going to have to stop picking through dumpsters. Our "core" is going to get sick of waiting and start demanding trades or wait out their RFA periods and bolt.
All it takes is one of Raymond/Seider looking at the parallels between how the Tigers and Wings are being run and saying "I'm only taking arbitration or a bridge contract to UFA" and the rebuild is dead. Or Larkin demanding a trade so he can win a cup before he needs a walker. Or Cossa busting and Augustine pulling a Petruzelli.
Yzerman inherited a dumpster fire but waiting for the dumpster to burn to the ground before building a new one out of Legos is not the most inspiring approach.
Edit: Cossa will likely not be an NHL starter for 3 seasons unless he blows the doors off the AHL next year. Full season starting in the AHL, one season as a backup in the NHL, one season as a 1B in the NHL. Acquiring a guy like Ullmark/Bishop/Saros and then resigning him for a few years isn't a terrible move, especially if Augustine doesn't hit and we can work it to where Cossa comes in backing up and the older goalie is willing to work in a 60/40 split when he's older. The days of NHL goalies regularly playing 65 games a season is over; you pretty much need to run two quality starters these days.
Who am I kidding, though, we're going to see Husso letting in 5 goals every game again next season.