First contact protocols could have been written in advance, with prepared speeches for when they first encounter an unknown alien, which they do, and Archer just wings it. Archer is a known anti-Vulcan in his sentiments and does not hold their best interests, as an ally of Earth, in mind when sharing military secrets to Vulcan's enemy. As
@eschaton notes he routinely ignores T'Pol's advice.
You want to write him over his head that's fine. But there's over your head and the unbelievably incompetent. I would trust Colonel Blake over Archer. Largely because there are Earth ship captains who could have at least a measure of understanding of surviving in space, of encountering the unknown, like pirates, and presenting a cool head as a leader.
I think it can be written well, simply by studying old naval logs and encounters by maritime explorers. Not perfect but at least a measure of competence.