Of course but the question is what could they do with Chychrun instead? Could they get an useful piece or nice futures to restock the pool? Most likely so it's either get nothing (with your proposal) or get that and deal with maneagable cap hits :
$333,333
$833,333
$1,833,333
$2,333,333
$1,333,333 x 4 years
Outside of year 3 and 4, very manageable.
I already mentioned the reasons, Chychrun is a piece you can have for 10 years, of course it's assuming they would want to extend him long term.
In the proposal, they dump Athanasiou which cap hit is higher than Korpisalo so dump for dump for the first year. It would mean only 3 years of taking Korpisalo's cap as an expensive back up (instead of signing someone for 1 M$ for example) but behind Mrazek with no pressure, there's a chance he does relatively better than he did this season. In the process, they replace Murphy's cap by Chychrun
Really a no brainer for Chicago... they have seen Chychrun when he was with the Yotes so maybe they see him as a building block and in that instance, they get him for not much...