One thing to consider here is that Archer's crew breakdown probably isn't particularly representative of what Starfleet intended an NX class ship to have.
After all, Archer left for his initial mission in a hurry, intending only to shuttle a Klingon prisoner/patient/passenger to the Klingon homeworld and then to return. We know he essentially left his main armament on the pier, and only had parts of it installed in "Silent Enemy". Events just conspired to keep Archer from returning to homeport for the next two years, so he had to do with the eighty people that had boarded the ship from the intended milk run.
Archer's second mission in turn involved special arrangements such as MACO rather that Starfleet ground-fighting teams, and could once again be interpreted as running contrary to most Starfleet ideas on NX class crewing.
Comparing with the only slightly larger TOS hero ship, eighty is probably on the low side for the ideal crew complement; quite possibly Archer's crew isn't officer-heavy, but enlisted-light. He's got all the officers he needs, but those officers don't have the petty officers and crew they would usually employ in executing their decisions. Thus, Reed has a very hands-on approach to weapons maintenance, and when he gets help, it's from fellow officers rather than dedicated gunners and mechanics.