OOUI was originally created with a classic design for buttons and other fields, and that theme (now called 'Apex') is still available and maintained. https://doc.wikimedia.org/oojs-ui/master/demos/?theme=apex We could switch to it at a moment's notice. Personally I wouldn't mind seeing it again ;)
Still, buttons in the default theme are not entirely "flat", they have at least borders (or strong backgrounds) to distinguish them. The biggest problem is the existence of 'frameless' buttons (in both themes), which look just like normal text if they don't have an icon or something.