Steve,
You have pointed out the crux of the issue and the inconsistency of the government's role: What does intimacy have to do with "marriage" in the LEGAL sense? There is no law requiring intimacy. So why is government in involved? Consider the government's awkward position on a foreigner marrying a US citizen for the sole purpose coming to the US. The US has made such a "sham marriage" illegal with pretty heavy punishment. What makes a legal marriage a "sham"?