Ok so I'll answer this from a hypothetical perspective.
First off we can assume that the fairies that actually heal Link and talkative ones like Navi, are actually different. Navi, Tatl, Tael, and the fairies in Phantom Hourglass, are all intelligent beings that help Link a great deal. Fairies that heal Link seem to just exist with no other purpose. In Ocarina of Time they're referred to as "Fairy's Spirits" and I think that's a pretty accurate description. This is even further supported by Majora's Mask's Stray Fairies, which are basically broken remnants of a complete Fairy.
As to the reason why Navi doesn't heal Link, well I think can be explained rather easily. First off, there is definitely a hierarchy among this race. Great Fairies > Fairies > Fairy Spirits. Great Fairies can gift Link with certain abilities as well as healing. Fairies display intelligence much like their superior counterparts, but don't have much of a physical form and they can't do much beyond offer wisdom and guidance. Fairy Spirits purely exist to heal Link. Notice how when Link uses a Fairy Spirit that the actual spirit doesn't exist after? It's almost as if that Fairy has given its life/power tool heal Link or that Link has taken its power. So that's the main difference between these Fairies and Navi really.
The question is whether these Fairies are sentient or not. I think I'd lean more towards not and I'll explain why. Again it's similar to Stray Fairies. Fairy Spirits seem to be an extension of a Great Fairy's Power rather than an actual inherent poor. It's as if she's giving Link a part of herself.
