Don't all modern houses have a decent mechanical ventilation system? In my experience, mold is mostly an issue for older houses, which tend to have lower energy efficiency. Bad insulation does nothing to prevent mold, and if your insulation is so bad that you don't need mechanical ventilation to prevent mold, it means the wind is blowing through your house.
So just get your energy efficiency as high as possible and use proper ventilation.
No, a large number of houses (at least here EU\Italy) is not "re-built" they are (badly) adapted with increased insulation (and usually with polystirene or styrofoam "coats" - please read as waterproof insulation) and - often this is the key issue - new windows that are air tight without retrofitting "proper" mechanical ventilation systems.
And it is not uncommon to find newly built (in the last - say - 8-10 years) houses that are in energy classes C, B or A that still miss such a system or having it not providing enough air changes.
Hence I earlier said:
>unless a proper (and properly calculated and maintained) mechanical ventilation system is installed
As a matter of fact mould is usually not an issue for older houses, exactly because the walls are not completely waterproof and because of the leaks from windows and doors (that even without having wind blowing through do allow some ventilation), there may still be localized mould where thermal bridges are, but is usually a minor issue that can be solved.
Recently (again last few years) some "new generation" of "local" (as opposed to centralized) ventilation systems (basically a fan with a heat exchangers that fits in a pipe 100-160 mm for which you bore a hole in the outer walls) are becoming a needed retro-retrofit to these houses but they tend to be a little noisy (so you need timer controlled ones for bedrooms).
To this you add ineffective, amateurish or no repairs and maintenance and you have the perfect disaster.
It is perfectly possible to build a long lasting, maintainable, underground house, but you won't have it "cheap", expect the costs to be between 150% and 180% (if not more) of the "normal" costs for a comparable sized house built with whatever building technique is common in your area (bricks/concrete/etc.).
Mould is almost unavoidable in any (not only underground) houses with a high level of energy efficiency (in Europe those that would be classified B or A and higher, even if in my experience issues start happening at the D or C class) unless a proper (and properly calculated and maintained) mechanical ventilation system is installed.
Though you may save over the years something in heating/cooling costs, it is simply (usually) not worth it.