I fought using both strategies and although I do agree with you, Jobo, it requires a higher degree of energy to 'bounce' for the entire match it also allows for more explosive 'in and out' or 'side to side' movement. If you train to bounce while you fight, you are essentially carrying your weight on the balls of your feet, using them like springs to move yourself. It is extremely difficult if not impossible to do this with the weight distributed to the entire foot. The timing and coordination would be completely off.
As I would be considered a heavy weight or light heavy weight, I do find it an advantage to use this tactic on fighters who do not bounce as they are not typically used to dealing with other heavy weights that are more nimble on their feet. If done correctly, a fighter that bounces can look much faster than their opponent but as you said, the energy drain is quite a bit more and so having good cardio is essential to employing this tactic.
As I am getting older and am not competing any longer, I do not use this tactic for an entire match unless it is absolutely necessary. I favour a combination of 'bouncing' and solid footed footwork in most matches now. I still use the 'bounce' when doubling up kicks or when I need to perform a Sabaki movement to get to the side but that is not to say that I prefer it to 'bouncing' for the entire match. The need to 'bounce' for an entire match is not necessarily required for each sparring session I do now.
Finally, I am not sure I would say that 'going up on your toes' gives you less stability. I find my stance typically goes wider when I bounce and have not noticed that I lose any more stability. Maybe I do but I just haven't noticed it.