Reviewing some basic principles:
A house with high thermal mass and low insulation will be at a constant temperature that is the average of the high and low temperatures for the last few days. In a desert climate with daily low at 70 deg F and daily high of 110 deg F, the house will stabilize at 90 deg F. I saw exactly these high and low temperatures in the US Air Force barracks at March AFB when the barracks air conditioning failed. The building was concrete block with no insulation. It took some effort to convince the guys that we should shut down the ventilation fans during the day, and run them all night. That kept the barracks temperature down to about 80 deg F, which was reasonably comfortable with the low humidity in that area. The AC failed at the beginning the summer, and was repaired at the end of the summer.
I toured an earth sheltered home in Illinois, a warmer climate than my home state of Wisconsin. It had minimal insulation, only 2" of foam around and over the house. There was no insulation underneath the house. The owner needed to add a second furnace to keep it warm in the winter.
A house with low thermal mass and low insulation is just plain miserable to live in. I lived in such a house for two years. It was impossible to heat or cool all rooms to the same temperature, so the house was never comfortable. There were many days when the furnace ran at night to keep the temperature above 70 deg F, and the air conditioner ran the following afternoon and evening to keep the temperature below 78 deg F.
A house with low thermal mass and high insulation that is thermally connected to the ground will stay cool in hot weather without air conditioning. My workshop in Northern Wisconsin is such a building. It started as a garage built on a concrete slab. The walls are insulated to R35 and the ceiling to R80. The heating thermostat is set to 66 deg F, and the indoor temperature has has never exceeded 70 deg F, even in an extended spell of 90 deg F temperatures. Much of the heat to get it to that temperature came from the dehumidifier.
A house with low thermal mass and high insulation that is thermally isolated from the ground with 4" of foam insulation under the crawlspace, under the foundation, and around the foundation walls needs air conditioning to keep the temperature down to 78 deg F after several days of 90 deg F and hotter temperatures. This describes my current house. It was a significant effort to get a central air conditioner that was small enough. It is a one ton (12,000 BTUH) unit that is actually oversized for this house. This house has even temperatures throughout the house regardless of the temperature outside. The comfortable house is the primary benefit, the ability to ride through a power outage or furnace failure a secondary benefit, and the low heating bills are a bonus.
Earth construction makes sense in moderate temperature, low humidity climates.