That right there is the biggest reason and/or issue. Even if the illegal isn’t voting, the census does affect the representation of a district, city, state, and at the federal level. Why should an illegal immigrant, not afforded an actual vote, still be able to affect the representation of a region?
Second, last I checked...no one actually checks the truth of the questions asked. So why wouldn’t they just lie anyway?
You could always revive the Missouri Compromise;-)