IMHO, the biggest hurdles to a quality stone house are the cost of experienced masons, followed closely by insulation and seismic safety. If you have time to develop your skills and have a strong back you can jump the first hurdle and can deal with the last two with some design workarounds.
Many historic homes and buildings are plastered inside, so maintaining an "authentic" look can be confined to the exterior finish. Insulation is really only a significant issue if you are insistent on keeping the interior face of the stone uncovered. Double wall construction allows the insertion of insulation in the gap while showing a stone finish on both exterior and interior walls.
Most modern stone buildings I have seen use stone only for an exterior veneer over conventional stud (
wood or steel), reinforced block or
concrete walls. This solves or reduces both the insulation and the seismic safety issues. For seismic safety, interior stone veneer tends to be limited to very thinly cut natural stone or lightweight cultured stone products. I live in an area considered to be at high risk for seismic damage, so codes reflect that. Other areas will probably be less stringent, but remember that there really is no such thing as a "safe" area when it comes to earthquakes.
I think that in cases where local stone is readily available, preferably on site, it
should definitely be considered as a building material, especially for fences, retaining walls, paving and outbuildings. When it needs to be transported and/or you need to hire skilled workers, you begin to quickly lose any economic advantage.