When I applied to college I applied to Missouri, Texas at Austin, Wisconsin at Madison, Northwestern, and some other school I can't remember. I got accepted into all of them.
Northwestern was the only one that I actually got a teacher recommendation filled out for, because they required one.
I looked at the Illinois website, and they don't ask for any teacher recommendations for admissions.
Some real talk. Universities don't care about what your high school teacher or guidance counselor say about you, as they're probably no name guidance counselors and teachers. If you can get a letter of recommendation from someone who these universities will recognize as an important person, then that could carry some weight (hey...what's that clout admission scandal going on....)
Pretty much what most of these schools do, in particular these big state schools, is that they break you up into three categories. In state, out of state, and international. They have a certain percentage of each which they accept. Not sure how it is in Illinois, but Texas was 91% Texans, 6% out of state, and 3% international when I applied. Some of these schools that have you declare your major will then separate you into categories for which school you're applying for.
Then the out of states are even broken up into states (and internationals into countries). So if you have some good stats and you are the only one in your state applying for a school, you're going to get into that school.
For Illinois you're in state, so none of that matters. Basically they will just look at your ACT score and your high school class rank percentage (top 5%, top 10%, etc.). That's the main deciding factor. They have some system of charting the ACT score against the high school class rank percentage to give you a score. If you meet a certain score, you are basically accepted. They will of course look at your essays and other information beyond those stats. So if you write some dumb crap in your essay, or got in a lot of trouble in high school, you could still get rejected, even if you made the stat cut.
For those who have borderline stats, those get put into a separate pile, and are looked at again after all the shoe-ins. This is when they start weighing stuff like extracurriculars, letters of recommendation, and essays.
Since Illinois is a big state school, they probably don't want to deal with reading a bunch of useless letters of recommendations. You'd have to be a pretty bad student to get a bad letter of recommendation from a teacher.