They’ve got drawbacks, too, especially since most examples of them in residential construction are the efforts of, shall we say, enthusiastic amateurs.

1. Because soil holds moisture for an extended period of time, they tend to get saturated, and then excess moisture migrates down to the waterproofing system, which will inevitably leak over time. Most amateur-built earth sheltered homes are not using particularly sophisticated waterproofing materials, and rarely take a defense-in-depth approach to them that could mitigate a failure in one layer of the system.
2. Maintenance is expensive: once any part of the waterproofing fails you are going to have to dig it up to repair it.
3. Soil - especially wet soil - is heavy and the prescriptive structural parts of residential building code aren’t really intended to address this kind of construction. You need an engineer to ensure the house is properly structured for the loads involved, and if you’re building new that extra structure is going to cost money and limit design options.
4. Building into a slope to allow roof access for planting, mowing, etc., limits daylighting options, and particularly in the US where bedrooms are required to have an egress window it can be nearly impossible to design a floorplan with the expected gradient of public to private space.

Don’t get me wrong, I love the concept, and I’ve even drawn up plans for one I’d like to build on the lot next door to me once the nigh-derelict rental house currently occupying the space gets condemned… But this is one case where I absolutely do not want to be buying somebody else’s project. I don’t trust the other people who build them to do it right.