It only applies to that Legendary Melee Weapon just as the DPS on a bow/crossbow only applies to the bow/crossbow. If you never find yourself being near a mob for meleeing then feel free to keep doing what you're doing and don't put points into it.
Originally Posted by Difious
I, however, have always been in plenty of situations where melee helps a lot. You can toss a low-cut between Rain of Arrows when AoEing mobs. I put Low-Cut bleed chance legacy on my melee weapon and also AoE targets. Makes for a lot of combo melee and ranged AoE dps.
There's also situations like Battle for Erebor where raid leaders will want you to be on a melee only boss (i.e. reduced incoming ranged damage buff on the mob). So it's not always smart to neglect dps on your melee weapon.
Chromite/Grumbletocks/Grumbletunes/Schrade on Landroval, Chromite on Arkenstone, Appendage on Brandywine