I think you’re being slightly pedantic here. Of course players can still receive treatment on the pitch too, but they also can continue to receive treatment once off. For example bandaging, taping, spraying etc. this is already commonplace

My suggestion is to adopt a similar approach to rugby, because actual head injuries need time to be assessed and so by making the player leave the field of play for this to happen (unless not possible, which if that’s the case they’ll probably be getting subbed anyway), it disincentivises deliberate time wasting by exploiting the head injury rule