Uhm, no? That's quite a leap you made there.

For a normal human with no health problems affecting their oil production/smell, if you aren't using shampoo/conditioner to constantly strip the oils from your hair, you very quickly stop overproducing oil.

Bedsheets and pillows should still be washed regularly, since they definitely get covered in excess skin oils/grime/etc.

But as long as you are caring for your hair in other ways like brushing daily and keeping it away from food/grease/mud/etc, using soap isn't necessary unless you actually soil it - rinsing is enough to get rid of sweat buildup.

Obviously, if you are working something like a trade job, its not possible to avoid debris, grime and other things and you need to wash your hair more, but an office job? Retail? Just brush and rinse regularly, and your hair will smell and look just fine.