You must voluntarily file to pay the use tax in Illinois.
I will never volunteer to give money to any government. Screw them.
Actually, you don’t “voluntarily file”, you are required by law to file.
It’s just that, since the companies cannot be required by law to REPORT their sales to you (since they are out-of-state and have no business within the state for the state to harass), the state has to depend on the ethics and morality of the citizens.
And as you demonstrate, morality isn’t really in play any more. It’s whatever you can get away with these days. If they can’t catch you, break the law. Nor moral or ethical, but it seems to be popular enough.
Missouri randomly audits businesses for use taxes and if no evidence of payment is shown there are fines, penalties and interest due.
They do have ways of finding out that you've purchased big ticket items out of state and can go after you if they think there is enough money in it. Repeat after me: "Penalties. Interest. Interest on the Penalties." It doesn't take long for the few hundred dollars you own on a big ticket purchase to turn into thousands of dollars that your state can take from any refunds you are owned or garnish from your wages if you refuse to pay. The odds of getting caught are low put the pain if you do is potentially quite high.