I started doing that a long time ago, I think I’ve even mentioned it here a few times over the years.
However, I just got new glasses and looked at their website to see what they suggested for cleaning. They said not to use soap, laundry detergent(?) or other cleaning products as they can strip coatings off the lens. So I tried their method, which was just rinsing them under warm water and drying with the included microfiber cloth. My glasses weren’t that dirty yet, but it appeared to work well.
I’ve been using pre-moistened lens cleaners and dawn since forever, and, while I don’t know if it’s related, but the reason I was replacing my previous glasses was because the coating was coming off which made them feel like they were always dirty.