Why does "love child" imply "out of wedlock"?

You can't really change the meaning of a word to suit your taste. "Love child" refers to a child born to parents not married to each other, and that is what people take away from it. If you ignore what others think and only pay attention to how you mean a word, you will cause your listeners or readers confusion or merriment.

(Incidentally, the word "love child" carries the same stigma in some other languages as well. 愛の子 (ai no ko or "child of love") means exactly the same thing.)

EDIT

Answering OP's question about how did it come to have a negative connotation. From Wikipedia article about Legitimacy:

At common law, legitimacy is the status of a child who is born to parents who are legally married to one another, or who is born shortly after the parents' marriage ends through divorce. In both canon and civil law, the offspring of putative marriages have been considered legitimate. For the opposite of legitimacy, the term illegitimate has been used about a child born to a woman and a man not married to one another, though in many societies today such terminology has become obsolete even in law, and abandoned in common communication in favor of less abrasive words such as extramarital or love child.

Illegitimate is a pejorative term, and, euphemism or no, love child ultimately inherits that meaning from its ancestor.

Love child can have a rather negative meaning because for a very long time almost all societies on Earth considered making love outside marriage as a shameful thing, especially for girls. She could've lost any chance of marrying at all if it became public knowledge. And a child, born from such an alliance, is the surest way to make it public knowledge.

There are lots of dramas in literature that illustrate my point. Walter Scott's "Betrothed", Griboedov's "Woe from Wit", "The Headless Horseman" by Mayne Reid and others.