Is there anything preventing me (other than common sense and logic) from building a home on Antartica?
Yeah, various international treaties on what can and can’t be done on the continent. AFAIK thatmeasn that private citizens can’t own land there. which means your house would be an illegal dwelling. And even if you could squat there you would need to spend considerable sums of money enuring that your house met the standards for pollution, emmisons, quarantine and so forth.