The hawks need 2 Top-4 D-men and a Top-6 forward to become again competitive... on the free agent market to get all that will require ca. 13-15M. And they must retain several coming up. So... no, you are right, if the roster stays basically the same as now (or changes w/ cheap options, the Cap is not an issue --- but making the playoffs will be unlikely. If you are looking for the team to improve its roster, it must shed many millions as we have many guys playing way, way, way below their Cap hit. And then we need to get no less than 3 major guys.
So... Cap issues are the thing that prevents the Hawks from becoming competitive.
Are you just assuming the Hawks will have 0 player development? Seems that way.
Forsling will hopefully take the next step so there is one of your top 4 needed. Pair him with Murphy on the second pairing. HJ will most likely be signed and while I would not hold my breath that he will be ready at 19-20 I do think he could work next to Keith. Bottom pairing you have Dahlstrom, Rutta, Snuggy, etc. Longterm you have Mitchell, Krys, and others in the pipeline. Seabrook is Seabrook.
Top 6 is much easier. 12/40/48/DS/91 are all player who could take the next step and play next to 19/20 and 8/88. For balance reasons I would roll 20-19-12, 40-8-88, and DS/91-15/48. You also have players like 64, MH, Fortin, etc. that are in Rockford developing.