I would immediately like to state that something in the OP is wrong. The majority of the games offer no subtle or in-yo-face hints about Link's romantic intentions or feelings. The only games that I've played that do this are Twilight Princess, Skyward Sword, and perhaps Ocarina of Time with Saria - but that was very vague. In the rest he is equally close with everyone it seems.
I believe that there are two possible answers to your question. It's either because Nintendo's target demographic are too imature or young to handle/comprehend a complex, classical relationship in a video game, or, Nintendo doesn't devote enough of their budget to the storytelling in Zelda so a romantic relationship never explicitly developed in any of the games. Both seem reasonable and possible, but are equally unacceptable.
You don't have to be eighteen years or older to enjoy or respect a classic, yet subtle romantic relationship between two people in a video game. Let's take Skyward Sword for example because, so far, that is the best example we have for an explicit romantic relationship in Zelda. Now, the game did an excellent job of dropping subtle hints throughout our journey to imply that our hero had a romantic interest in our beloved Zelda. The hints were placed right, did not interfere with the gameplay or conflict between Link, Demise and Ghirahim. At the end of the game I was so ready for Link and Zelda to just simply kiss. . . but it never happened. WHY NINTENDO WHY???? A simple kiss would have resolved the romantic tension between Link and Zelda, it would have satisfied the player (don't tell me that you didn't think it was going to happen too), and it would have offered so much more emotional connection between the player and the game (like there wasn't enough of that already). A simple kiss at the end could have done so much more for Skyward Sword, but they chose not to add it, probably due to one of the aforementioned reasons I mentioned above.
Typing this also reminds me of an excellent example that Nintendo could adopt for future Zeldas. This example comes from Avatar: The Last Airbender. Now the majority of you have probably seen it, so I'm not going to rehash the entire relationship between Aang and Katara. The point is, for those who have seen it, that show did a stupendous job of combining a rather complex, deep romantic relationship between two main protagonists and action/adventure. How was it resolved? A passionate kiss at the end between the two. Nintendo - learn from them.