Because I have to tie the 2 power supplies together to form a common ground so that the 5V one will be interpreted as negative voltage. That's fine if the PS are isolated but the vast majority of the ones I've seen are not. However, that dilemma was kind of solved at the end of page 1 so if I want to fork out 3-400 bucks, I can get a relatively compact dual PS that's isolated.
I understand all about heat. As I said, I've already constructed a "dumb" power supply with the exact same op amp. It doesn't have any control logic, just on and off but other than that it actually utilizes the full 10 amp limit of the chip and with a modest heat sink and desk fan I had it charging my car battery and I didn't burn my finger touching it. If I were to use the "smart" circuit to charge the same battery the only thing that would change is being limited to 4A for starters and all the additional features the board is capable of. Now if I were using FETs in a switched mode setup, all that fancy pulsing in my logic would put the FETs into linear mode more of the time, producing more waste heat than usual but with an op-amp that's already running in linear mode, it's exactly the same as my dumb charger... same heat dissipation or less (because it's capped at 4A). Basically I don't foresee a heat problem. After all, the op-amp IS designed to pass 10A at full supply rail voltage. It tells you the thermal characteristics under that scenario and what sort of thermal conductivity your heat sink needs to have and what your duty cycle has to be and all that so as long as you don't violate any of the limits of the chip and you have a good heat sink, why would it blow up?