Could you see anyone as Túrin's friend?
Beleg yes, but that took time and effort by him. Why would Faramir wish to invest his life for him? There was a narrated destiny for Beleg to give his life for Túrin but I think Faramir had other causes to care and live for. And would Túrin have accepted anyone that close to him unless they were really giving their lives to him (just think of what Beleg did)?
One can't just keep up "nice relations" with tragic characters like Túrin?