Specifically, within the sentence "to sing along to/with", can to/with be dropped freely?
While searching for information I found out this seems to be an idiom, so possibly my question should be extended to: "Can common prepositions following a verb be dropped freely when used within an idiom?"
The full sentence which inspired this question was: "But I'll write a song for one day we'll sing along". The intended meaning behind this is the following: "I will write the song, and here's why: one day we'll sing it together". The original phrasing sounded incorrect to me both in regards to the usage of 'for', as well as it sounding weird since 'with' or 'to' is missing.
The question is whether or not this is grammatically correct. Can the phrasing 'sing along' be used without 'with' or 'to' following it?