The reason why Hart makes a lot more sense than Saros or Hellebuyck is how he potentially meshes with Levi. He's that much younger, with far more team control.
You trade for Hellebuyck or Saros - you're obliged to give him a big money, long term extension which likely also includes a NMC/NTC, well into their 30s. Therefore locking him in as your long term #1 starter who gets 60+ games a year. May be a good thing since both guys are elite - but at that point... You may as well trade Levi because there is no space for him.
That wouldn't be the case with Hart though. You're not obliged to give Hart that type of extension. You see how both he & Levi do this year before deciding what to do. If Hart plays like an elite starter right away - then great - you found your guy. But you also have flexibility. If Levi emerges ahead of him - team control allows you to bridge Hart and potentially trade him further down the line. The only risk is that he is terrible from day one - which is very unlikely - but even in that event all you lose are the assets given up to acquire him.