Though the term “cover version" wasn’t coined until 1966, the practice of covering songs is officially recognised as having started in the early 20th Century.
And yes, its roots were inevitably fiscal – it was used a way for record companies to cash in upon the successes of another company’s tunes.
Even now, copyright law does render the practice financially beneficial for songwriters and publishers – they are paid royalties for broadcasts of covers, though artists are not.
O is also for... Obnoxious: Some cover choices are just plain ill-chosen. Avril Lavigne’s version of Coldplay’s The Scientist and Gossip’s take on Careless Whisper both spring violently to mind.