It seems to me people are very insular in their ideas based on their airfield circumstances. In my opinion on a very long runway your actions may well be different to those if you were in a similar circumstance on a very short runway. Similarly you may have to deal with a bounced landing asymmetric or indeed counter and react quickly to the bounce from a glide approach with power unavailable.
It has been my experience (instructional 2000+ light single /twin and 5000+ multi military) that most students and inexperienced pilots unfortunately cannot think/reason in a high stress situation. A normal landing is such an event and if they bounce then hand/eye/foot co-ordination invariably fails and a situation akin to panic takes over and all normal handling techniques are abandoned in the attempt to try and bury the prop in the ground. Life is surely worth more than $30 and therefore in the early stages of learning there should only be one course of action until experience is gained and that should always be safety first, ie to initiate a go around.
As experience is gained and depending on the students’ personal ability then they can be introduced to dealing with PROPERLY RECOGNISED AND DIAGNOSED over rotations, flares or minor bounced landings which might still result in a go around.
Horses for Courses and there is always more than way to skin the cat/dingo/possum/gougar!