As much as I agree with this conceptual idea, I don’t agree with the implications for OP.
OP - Please go talk to actual CS students who are going through internship/job search hell right now. Ideally, talk to Raikes kids as well as UIUC CS kids. Ask them how their recruiting is going (One shortcut is to look for “incoming SWE” and filter people on LinkedIn currently at both schools).
Personally, talking to a wide range of CS kids in my circle (schools include Berkeley, Waterloo, UW, Other UCs, UIUC, Some CSUs) - school name has played a much greater role this recruiting cycle given the 1000s of applicants for each role. Before you get to an interview where you can showcase your soft skills, you need to get through resume screen - a step where UIUC is going to have a greater degree of impact than Raikes.
It looks like you want to to go to Raikes, but I recommend you do more homework on outcomes before giving up UIUC. Its pretty easy to add business degree to a high quality CS education down the line. The reverse is impossible.