So far as we know he doesn't, polite generosity aside. Realistically if he tried to he'd be spending over 75 % of his waking time I'd imagine, and still wouldn't get to everything. But he has said that he has to keep his focus on his family and friends, they are his primary responsibility, he can't let himself get sucked into his fans' personal world/lives. With the sort of temperament he appears to have this is understandable, as he would find himself concerned and ensnared by the problems and concerns of those who wrote those kinds of fan letters. So better that he not do any of them, than try to separate the ones that didn't want something from him from the ones that did.
This doesn't mean that he doesn't read, just that he doesn't respond :). Anytime a fan writes to their 'object of affection', they should do so without expecting a response - just say what you want to say and be satisfied that they read your words. Make it a one-sided 'conversation':). No expectations, no disappointment - if you do happen to get a response it's a nice bonus ;).