You said "I know what 너였으면 좋겠어 means", but my impression is,,,
In this context, '너였으면 좋겠어' refers the future.
I(the singer) hope it is you who hugs me when...
'...안아 줄...' is a future event.
If you take '너였으면' as the past or present as you put 'i wish it was you',
it means another hot guy hugs me(the singer) every night.
So the singer is sad, because it is not you who hugs her...lol
The singer imagined the future event has already happened in her/his mind.
'너였으면' is more emotionally ardent or earnest than '너라면' which is simple assumption.