Songs Not Eligible For Oscars?

I'm guessing that, since this was first a stage production in a prior year, these songs don't qualify for Academy Award consideration. Has this always been the case? So many great musicals began on the stage, The Sound of Music, My Fair Lady, Cabaret, Fiddler On The Roof, Jesus Christ Superstar (actually first an LP.)

I liked the songs "When I Grow Up'" and "Naughty." The "Miracle" opener was better in the stage production IMO.