I used to have a thermoelectric cooler, but I found it had these issues, which prompted me to stop using it, bite the bullet and get a 12v fridge/freezer (Waeco Coolmatic CF-40):
1) As you've mentioned, it consumes A LOT of power. It cannot be left running overnight, or your battery will be dead the next morning. You will not be able to start your car, and after you do, you'll need to keep the engine running in order to keep your food cold during the day. Plus, if your car isn't parked in the shade, interior ambient temps will be well above 100° (making the cooler's interior temp a balmy 60° or more).
2) It can only cool to 40° below ambient. That is, the external heatsink on the cooler needs really good ventilation in order for the air around it to be the same as ambient. "Ambient" temperature in the cabin varies widely, especially in the rear cargo area, where the HVAC effectiveness is nearly non-existent.
3) If the items in your cooler are frozen (0°F) or are fresh out of the fridge (35-41°F), using the cooler will actually warm up the inside if the ambient temperature is over 75°.
YMMV. Report back how well it works for you.