Yeah, but I don't think cost a melee would be too bad. Usually the class goes Int/Disc, and doesn't care about its strength stat. I don't like it's acceptable to have melee better than your melee that doesn't cost anything. It would also make Insurmountable Skullfort good for Striker, so I thought that would be interesting. U do feel the other run perk, the one with a shield should get a tiny buff just so it can see play.
I just think the class shouldn't be able to use everything it has availible to its fullest. If you made shoulder charge cost a melee you could probably have a exotic made that would make it free and everyone would probably use it unless they wanted two grenades or a evade. The fact that the option would make it a higher tier exotic is exactly why it should get nerfed.