He did become a Jedi. A Jedi just means that you are no longer a Padawan. If you watch Star Wars: Clone Wars it shows that he did. Now that show is not actual canon, but you can assume something similar happened before The Clone Wars show began. What Anakin did not get was the rank of Jedi Master. George Lucas thought it would be good for the character to have a Padawan to help Anakin’s story arc, both in making Anakin more likable as well as helping show his fall to the Dark Side with her eventual death. Though that didn’t end up happening in the show, that was George’s intentions with her. Was it for female representation? Maybe, but it didn’t feel like that in the show. So whether it was or not, it was done right which is exactly what the FM wants.