They are not in the dictionary. They are not real words. They are not proper written English. They are "colloquialisms" heard in spoken speech. Writers can and do write them IN DIALOG, inside quotation marks. --The boy at bat called to Nick: "Heh, you! Wanna come on and pitch?" (Edna Ferber, "Gigolo") Edna Ferber is showing us that the boy speaks colloquial English.

Why DO WE NEVER write "wanna" and "gonna"? Cuando hablas inglés rápidamente (como un nativo), el sonido de "want to" suena como "wanna" y el sonido de "gong to" suena como "gonna" -- cuando se escribe o se transcribe un diálogo, se puede escribr "wanna" o "gonna" pero simplemente son formas de "want to" y "going to" del inglés escrito. En español se escribe "para que" pero en español hablado la gente dice "pa'que" -- un proceso similar.

As Dan says, we don't write them because they are not words. They are transliterations of rapid spoken language. To the educated native speaker they look lazy, careless, and rude.

" Why do we never write "wanna" and "gonna"? " - this is the proper way to ask your question. I think Dan's given a short and perfect answer. If you write "wanna/gonna" in your regular writing and expect us to accept it, you're basically admitting that you're not very good at English and you don't care.