I think that the long-term, team-friendly deals to which Hahn signed his core position players could/should make it easier to straight-up "buy" starting pitching even with a relatively tight budget.
Anderson, Moncada, Jimenez, and Robert will together cost $20.25MM in 2021 while Madrigal, Cease, and Kopech are all on pre-arb minimum contracts. Those four will be $36.6MM in 2022 with Kopech headed through arbitration the first time. Anderson has a $12.5MM club option in 2023, but that group would cost $50.1MM that year with Cease hitting his first arb year.
By contrast, Jason Heyward will cost the Cubs $23.5MM in 2021, $24.5MM in 2022, and $24.5MM in 2023 with enormous paydays coming up in the next couple years to Baez, Bryant, and Contreras (only slightly lower payday in order for Schwarber).
I can tell you which contract situation I would want if I were a GM and it's not the team I prefer.
I am not making an argument of Cubs vs White Sox. The Sox have the cost controlled, younger core right now that give them a better chance of keeping their current MLB together. What I don’t see is a clear pathway for the Sox to build on the current roster to create a World Series contender. Their Achilles heel is the starting staff. If they get lucky and develop a couple of high end starters then it could happen but I am not optimistic on Kopech. Cease I like but he is not enough. They need to hope that Hahn hit on his first round pick this year. His track record with the draft as White Sox GM has not been very good.