I have to reject your point because the recognition of Copyright isn't to encourage competition, but instead to encourage original creation (i.e. progress) by securing a monopoly for the original author over the original work and by implication any derivation. But in the arts it's difficult to create without some derivation, and so monopoly on copyright must be limited in time else it will eventually work to prevent progress rather than encourage it. Furthermore legal precedent recognizes "fair use" because there forms of original work (e.g criticism) where in order to refer to another particular work it is necessary to replicate the original in some form, but not wholly.
One example where copyright encouraged competition...
In the 80s, Compaq had to develop an IBM Compatible BIOS without infringing on the 9000+ copyrights held by IBM for the softwAre that comprised their BIOS. Compaq could not infringe on even 1 piece of copyrights softwAre or they would be in violation of copyright law. This forced Compaq to create all original code so they could compete in the then burgeoning computer market. Much of the softwAre they produced was better than the original IBM code which then forced IBM to also improve their softwAre in San effort to stay competitive. Additionally, all additional IBM compatible computer manufactures that did not license either the IBM or Compaq BIOS were forced to create their own BIOS softwAre. The fact that a copyrighted solution created a market opportunity and therefore competition in that market cannot be denied.
While it is possible that the intent of copyright law was not to foster competition, it did in this case.