I give June credit for making a gallant attempt in The Secret Heart. Can't agree that June has a very girlish face but maybe her rough sounding voice influenced me. Note that Joan Fontaine was born the same year as June (1917) and to me Joan has a lot younger looking girlish face than Ginger or June. (not that MGM would have gone out of their way to get Joan on loan out).
Either way I understand why studios would cast an experienced actress 10 years or more older than the actual character. It can be difficult to get a first rate performance out of a teen. E.g. Ann Blyth being 17 for Mildred Pierce pulls it off but otherwise why take the risk.
You don't think June has a girlish face in GOOD NEWS, made around the same time? Of course, it depends on the make-up I suppose-- but to me, she often seemed younger than her actual years.
Recently, I watched several episodes of The June Allyson Show on YouTube. They were filmed in 1959, and the other actresses in those episodes (Ann Sothern, Ginger Rogers and Ann Harding) looked good but were definitely showing their age. Not June. She was wearing beautiful gowns and had chic hairstyles and when they cut to a long shot of her entering a room, she seemed so petit. She would speak directly at the camera to introduce the story, and it was hard to believe she was a big star with her own show-- because she looked like the girl next door playing dress up, very delicate looking and soft (despite the husky voice).