I think it's all about your team's perspective.
I know it was an extreme example, but last year's Florida State team clearly did not think the bowl game was important at the time. Now, maybe they should have thought it was more meaningful, but that's a different discussion for a different day.
For Illinois, it was clearly meaningful. I know Pat Bryant didn't play, and I will still fully support that decision. But for Illinois, that was a big game. They were playing a SEC team in SEC territory. The game was on ABC. I didn't think the game was "win or bust", but Illinois had to come out and be really competitive in that game. If anyone thought the game was meaningless, Bret Bielema forever gave us proof that it was not when he played Shane Beamer like a fiddle late in the third quarter. I also think South Carolina took the game really seriously as they felt they had a gripe about not making the CFP and wanted to prove a point.
And I agree with you 100% that the Citrus Bowl was an incredibly consequential win. I think we had three of them this season - Michigan (always a statement to beat them, and they were the defending national champions), Rutgers (culture-defining win), and South Carolina (all of the reasons I've mentioned).