For show. These politicians already have the information they need.
Basically, as Frank has pointed out on his own, what they're after is a "Michigan State"-type counterpart to UIUC*. But they can't seem to get anyone motivated to build that on its own merit.
So the politicos publicly put on a show saying "We want to get a second state-funded university into the B1G". The B1G gives them this information (again, which they *already have*) to put in the public record, as though dangling a carrot in front of the Illinois legislature. This way, they also get an impartial arbiter saying "which university the state should push the money towards", rather than local politicos (and alums) jockeying to make their "local U" be the one that gets the gig; the B1G can come back and say "Well, we don't think any of you make the grade. But if we had to choose...".
Armed with this information (and put into the public record when the bill goes up for hearing), the politicians now have (a) a university to target with their plan and (b) the motivation for the state to make this happen (i.e. "if you do this, the B1G might consider this university for membership"). They quietly withdraw the bill they never intended to pass anyway, and put up instead the bill they always wanted to pass giving more funds to the "university of choice to be the state's #2".
Yes, it's all grandstanding for show.
*Yes there's already an Illinois State, but the gap in comparative quality between UI and Ill-St. is way bigger than UMich and Sparty.