This is a very personal topic for me, since some of my most intense and enlightening experiences have been associated with Priesthood blessings. I have had at least three experiences that simply can't be explained in any way other than the opening of the heavens and having divine messages delivered through my mouth. (I really mean that, and I guarantee that nobody could construct a reasonable argument with that conclusion if I did share the details.)
Having said that, I also believe strongly that there is a "gift" associated with healings. I don't mean a gift to be able to heal everyone of everything, and I don't even mean a "gift of healing power". What I mean is a gift to be able to ascertain the will of God in situations where the person will be healed or not healed - but where God has something He wants said regardless. I’m not certain it is a permanent and constant gift, but I am sure it is a targeted gift in those circumstances when He really does want to speak directly to the person (or even those listening). I really don't know how to describe it properly, but I do believe in it.
In my own case, there have been lots of times when I simply have not felt any particular inspiration - where I have not felt like a conduit for His words. In those cases, I simply have stated that I am the one blessing the person as a Priesthood holder ("I bless you . . .") and hoped that my sincere hope would be granted - and I have avoided making specific promises about healing. However, there have been lots of times when I have felt prompted to make certain clear and astounding statements - and often I have seen them fulfilled. Those instances could be explained away as just the natural healing process, and perhaps they were, but I take comfort in them, nonetheless. That, in and of itself, makes giving blessings worthwhile - and the possibility that God will, for whatever reason, rend the veil once every few hundred blessings makes the concept and the practice sublime to me.
I think ALL worthy individuals (inside or outside the Church) have the right and ability to bless others and pronounce promises of hope and faith, dependent on the will of God (whether through the Priesthood or not), but I am deeply thankful for my own experiences where the heavens opened and I spoke the word of God. It's hard to explain what that feels like, but I'm glad I waded through the "common" ones enough to experience the "uncommon" ones.