Modern "stick built" homes in the US are well insulated and actually quite efficient. Stone walls would be a poor choice in most areas in the US due to extreme conditions.
As you mention, once a stone house heats up in the summer, that is an incredible amount of thermal mass to cool. Your AC would run non-stop. Similar issue in the winter, super high heating costs in cold regions.
Heat capacity doesn't mean much unless the walls are several feet thick.
The frost line where I live is around 5 feet deep into the ground- meaning that footings for any building have to be that deep to avoid shifting as the ground freezes and thaws.
Summer months thick stone walls can be nice if you are able to keep humidity out, but if you don't and your walls actually stay cool you're dealing with a lot of mold and mildew since water will be condensating 24/7.
I don't know how thick a feet is, where we live we don't measure distances by the length of the feet of the king.
But I have lived for 10 years in a house with 30 cm thick walls and it has a tremendously positive effect, when outsite it is 30C and inside the walls are still 20C into July.
"mold and mildew"
Didn't have that problem in 10 years. This more happens with modern insulation than thick stone walls from my experience YMMV.
There's a fantastic service called the internet, which helps with things you don't know about. According to Google, 5 feet is roughly 1.5 meters. That means that the ground is frozen solid on average 1.5 meters below surface level in winter. However much thermal capacity your walls have, it won't be long before your attempt at heating or cooling your living space is competing directly with the outside environment. It is less of a concern in summer, since the difference between inside and outside is much smaller, but critical for energy usage in winter.
As for mold and mildew, you only get that with modern insulation if you have a poor envelope- i.e. drafts in the walls due to improper sealing. It's not the sort of thing drier climates have to worry about at all, but in very humid environments such as where I live, preventing condensation inside is important. That means not having walls that are cooler than the dew point of the air getting inside.
Basements here are very prone to getting mold or mildew, because (a) they have solid walls, (b) are kept cool via the earth acting as a heat bank, and (c) will readily absorb moisture through the stone or cement.
Most around here have some sort of sealant paint or active dehumidification running in summer to avoid mildew. If the basement walls didn't have to be load bearing, solid wall construction would absolutely be the last choice for basements because they're definitely the worst for thermal and moisture resistance properties.
Those walls would be nearly 30C in the inside already, if my house was built with them. The average temps for the past few weeks (low + high / 2) have been 30-32C. Its still somewhat early in the hot season here, so that will still go up.
There are months of the year where it doesn't get less than like 32C. save for rare cold snaps were it'll dip down to 26C or so for an evening or two.
My pool, which also has some decent thermal inertia, is already at 30C. The average temperature is still going up outside.
All of Europe is further north than most of the US. This does some big things for the climate.
As you mention, once a stone house heats up in the summer, that is an incredible amount of thermal mass to cool. Your AC would run non-stop. Similar issue in the winter, super high heating costs in cold regions.