I think any HTTP delays you see are due to the power controller itself, not the network device that you attach to it. There are reasons why you might want to use an Arduino with an ESP and not an ESP stand alone. For example, the ESP runs a network protocol stack that can interfere with real time response. The ESP is a 3.3V device and so needs circuitry to interface with 5V devices. Some Arduino have many more pins available than the ESP.
Also you are just turning LEDs on and off? How realtime do you really need that to be?