I always thought linking the sneak skill to the "sneak weapon" perks was a bit much, I figured the sneak weapons would just allow you to make sneak attacks with them and have different traits and maybe some different perks to normal weapons, the sneak skill already does so much without unlocking weapon perks, and like you said it kind of dwarfs the usefulness of going melee only. To be honest I thought at first that sneak unlocked perks on the stealthboy itself, but there are just the 3 traits.
Though going both means you will deal even more damage than with only boosting stealth, and there are still non stealth melee weapons that are plenty worthwhile.