The efficiency difference in a power supply running off 120V or 12V is not significant. The power supply is a negligible portion of heat output. They would last

The efficiency difference in a power supply running off 120V or 12V is not significant. The power supply is a negligible portion of heat output. They would last longer if separate though. Slim recessed LED fixtures have their power supply in a separate box. I.e. https://www.ledsupply.com/led-bulbs/slim-recessed-led-light https://www.ledsupply.com/led-bulbs/slim-recessed-led-light (arbitrarily chosen, not an endorsement)