It's worse than that. Of course, you don't actually "need" teeth to eat: you can just eat baby food all the time I suppose. But a lot of infections in people start in the mouth, and historically tooth infections were the cause of early death for countless people. There's a reason people needed bad teeth pulled in the days before modern dentistry.

And yeah, vision checkups are pretty important to: regular checkups find problems inside your eyes that will cause blindness later.

The US seems to do an absolutely horrible job of preventative healthcare. Here in Japan, everyone gets a free yearly health checkup that looks for all kinds of issues; it includes blood, urine, and stool testing, and also includes hearing and vision checks, abdominal ultrasounds, a chest x-ray, etc.