I teach my students to keep the feet on the floor and use only the top part of the foot, just like you.
The benefits are obvious. First couple of hours any student is nervous and keeping the feet on the floor prevents them from pushing very hard on the pedals. If they do, the fingers will start to hurt and they will release the pressure on the pedals.
Another thing is, when they are pushing hard on the pedals all the precision control is gone and you get slow but aggressive inputs.
So, feet on the floor it is.