AC isn't a problem if the energy feeding it is carbon neutral. With a strong mix of renewables and nuclear this is achievable, but instead we continue to burn coal and natural gas to provide base load.
The AC cools the house at the cost of many more KW.
The house gets cooler but this is all heat from the electrical usage.
The AC cools the house using about 3-4kW, total.
The roof on the house (assuming 29N because the article is about Houston, so between 10AM and 2PM, that's a Solar irradiance of 1kW/m^2) is receiving 157.9kW of sunlight, and then absorbing about 85% of that.