I see all sorts of answers online, but am not fully convinced. I tried finding some research on the longevity of clothes between wash and wash + dry. Considering that it dries for hours just the mechanical movement should damage the clothes I would assume?
Wife is always right! - Aside of the joke, I would attack this from an other point.
If the pants has a ‘permanent’ crease the dryer definitely will remove it, and the ironing will be a nightmare afterwards.
If you have garment bags you can always use it for the dryer, it would prevent some damage: stretching and so on.
If the price of your pants is less than a “disposable” amount for your family - probably not worth the hassle. If it’s pricey then honestly it is not that much more work to hang it on a pants hanger to dry. In that case it’s better safe than sorry.
I’ve heard stories about dry cleaners just using washing machines in the back, never got caught and got great reviews. So there is that. ;)