I think you would benefit from spending some time studying scales that are not related to any particular song.
The reason for this is that songs, particularly instrumental tunes but also vocal ones, often have notes that are not included in the principle scale. These are called accidentals (though they are quite deliberate).
You will also discover that tunes often pass through several keys. I am not referring to key changes that are indicated by a new key signature but key changes that come about because of movement in the harmony. For example:
Suppose you have a song in the key of C major. Somewhere in this tune the composer has written a C7 chord. Even though it is called "C7" this chord belongs in the key of F major. Effectively the composer has caused a key change.
Take an old song like Sweet Georgia Brown (The Harlem Globetrotter's theme song). This tune has 2 measures of E7, 2 of A7, and 2 of D7 in the opening phrase. Each dominant 7th chord implies a key change. You will not find the key signature changing every 2 measures however. This would make the score unreadable. But the musician who has studied his or her theory understands this movement of key changes.
Jazz musicians call these key changes 'Key Centers' and understanding this helps some jazz players memorize the chord changes to a colossal number of songs.
I don't want to confuse you with theory. What I have tried to do is illustrate a couple of reasons why it makes sense to study scale theory both in the context of songs, and out of it.
At the very least you should try to be aware that scale theory in song context may not be as pure as scales in isolation.