I call this build the Chop Doctor, the idea being to use unarmed combat and healing skills while minimizing inventory management by not having to worry about weapons, ammo, or pots. It's been mostly a success so far - combat's been a breeze and even with a low Charisma stat I'm raking in cash by trading off all my gear. The downside is I'm still heavily reliant on Stimpacks, as (perhaps because of low Intelligence?) my First Aid skill is weak. If I were to retry this build based on what I've learned so far, I'd take a point each off of Perception, Endurance, and Charisma, and crank my Intelligence to 8.
The other important consideration is that I've chosen Dogmeat as a partner, also effectively an agile unarmed combatant. This means we tear through small groups but tend to get surrounded, and if he ever gets split up from me (thanks to his rudimentary dog brain's unusual ideas about targeting) he tends to die fast. This isn't so much a downside as it means I probably need to adjust my play style.