a real wood burning fireplace is possible

There are plenty of small wood stoves made for very small spaces on the market. That is what you would want. If installed using correct clearances and you do not overheat the stove, I see no problem. But I have lived for many years in various wood-framed, wood-sided houses that used wood for primary heat. I prefer lp as I do not care to split wood anymore. I am getting lazy in my old age. I would think you would need to clean the ashes out of the stove and sealing into a metal ash bucket before traveling anywhere. I just remember having ashes al over the houses I lived in. I am in mid west NM and you can go up into the mountains and collect downed cedar wood for free.

As far as the folks who say they would not do the same.... well there are lots of things that some will not do that others will. Do your research. Learn how to use a wood stove safely. Learn how to install it safely. And remember, now "period" means "but this is not the last word, I will change my stand on this subject".