Ray Charles was a pioneer in insisting that he own the phonographic copyright on his recordings when he moved from Atlantic to ABC-Paramount yet this remained something out of reach for most artists. Robert Fripp was engaged in a decades-long lawsuit against EG to regain control of the phonographic copyright on King Crimson material (as well as to recoup illegally withheld royalties). Squeeze is another artist who re-recorded their albums to reclaim the phonographic copyright.
It's worth noting that Warner Brothers' response to Swift re-recording her albums was to update their contracts to prevent any other artist from following in her footsteps.