That's not a given, though. Lots of shows keep the same theme arrangement throughout their run. For instance, Stargate SG-1's theme was unchanged for ten years, except for the couple of seasons where the titles were cut short. Mission: Impossible had two different title arrangements, but at least one of them was used throughout the show's 7-year run, alternating with the second arrangement. The A-Team had the same theme arrangement for the first four seasons before getting a new one for the fifth. And so on.
And I don't think it's about paying the composer; the composer gets royalties regardless. It's about the musicians' union -- by limiting a show's ability to reuse music from earlier seasons, it requires the show to keep hiring musicians, helping them stay gainfully employed. Though that's probably not as great a consideration these days when so many shows have synth scores that are generally performed by their composers.