I agree with every word in your post. I think when it comes to discussing the greatest musicals of all time, it's important to put film musicals into categories. Love Me Tonight is a 30's book musical based on a play with a completely original score composed specifically for the film. I would compare it to other 30's musicals like Top Hat, Follow the Fleet, Swing Time, and The Wizard of Oz. In that group I would rate it pretty highly.
I don't think it makes much sense to compare Love Me Tonight to a film like Singin' in the Rain, which doesn't have an original score, or Oklahoma!, which is a film version of a Broadway musical.
Love Me Tonight was also made pre-code and (unfortunately) for censorship purposes apparently, it was trimmed of about 15 minutes of footage, which is considered lost.