We'll have to agree to disagree on this one. I can't speak to the thermal efficiency of log vs man-made, but I do know that many log homes are built in the southern Colorado area where it gets quite cold during their extended Winter season. I feel certain that these are built not just because of their inherent aesthetic qualities, but for their ability to shield their occupants from the cold and to withstand the ravages of both time and the environment.
As far as the environmental impact of the removal of the trees. I have mixed emotions. Luckily trees are (or at least can be) a renewable resource. They are a gift for us to use. Unfortunately, we negatively impact the environment for our own comfort. Have you checked on a concrete plant lately? How about the wood used in more traditional construction? The manufacture of roofing materials?
We have spent each of our summers for the last 30+ years in a log cabin which dates back to the early 1900s. Granted the construction is crude, but sturdy none the less. It would be hard to convince me that with the advances in construction technology that today's log homes are far more than second class structures suffering any more "inherent issues" than other forms of construction. It's just too bad that it isn't practical to have a log home built around here.
I must be honest and tell you that I'm not supportive of log homes. I have to admit that I find them elegant and very quaint. The reality is that log homes are not very good thermally. Wood isn't the best insulation we have available today. Also the amount of large diameter trees that have to be harvested to manufacture a log home is just too much for me.
That said a lot of them are built every year. The issues you mention are not going to be cured simply by building a log home. The problem is indoor air quality. You can consider building a very beautify energy efficient home that if completed along green building guidelines the toxicity issues and poor indoor air quality would be resolved and ease the respiratory problems you are experiencing.
Log homes also require a tremendous amount of maintenance. As the logs dry out they crack often with cracks open to the outdoors. These then have to be caulk filled. As the logs cure every critter known to man attacks the wood. The cellulose fiber is a food source for all boring insects. Molds, mildew, fungus can take root on the dark moist areas at the base of the walls or on the north sides. Typically, the logs need to be repeatedly re-sealed. Often log manufacturers impregnate the logs with insecticides, mildicides, pesticides and preservatives to ward off the hungry critters.
None of these are good for human health and vitality.
An interesting historical note - as soon as the pioneers could afford to build a home with bricks and sticks the log cabins were abandoned pretty quickly. These were smokey, drafty, dirty, rotting places. New cabins certainly aren't the same but they still suffer from other inherent issues!
Gary Gene Olp, AIA