This is a very complex concept, and there is no one answer.
Based, in part, on the belief that innovation is not possible under perfect competition, many scholarly papers are written about how monopolies and oligopolies affect innovation; yet, innovation, and the subsequent adoption of new goods and techniques could be defined as technological change that thrives on perfect competition.
On one hand, much of the history of innovation exists without copyrights, patents, and other forms of legal monopoly. As such, innovations take place in a competitive environment with or without intellectual rights being claimed. Such—free—ideas have value when they are embodied in goods or people, not intellectual monopolies. Yet competitive equilibrium without copyrights and patents tends to fail because because ideas are indivisible, and not tangible.
As such, when new ideas are built on old ideas, intellectual monopoly by one or more interests may lead to even less innovation than when there is competition. The theory of the competitive provision of innovations illuminates why markets thrive on competitive innovation. If intellectual property rights are cancelled, there is a trade off of long-term growth for more current output. Or, there is a trade off of current output for a more long-term growth when intellectual property rights are strictly enforced.
It is important not to confuse free markets with perfect competition. Free markets means free entry for new firms and/or products into the market. That said, free markets are far more helpful to innovation than perfect competition. Perfect competition is not conducive to rapid growth because growth is ultimately driven by innovation. People innovate if they have a reason to innovate, and profits are a driving reason for innovation. Nevertheless, such profits only exist when the innovator has a market share of power.
In conclusion, the paradox of your questions is that perfect competition maximizes the output of existing products. Yet, without patents for existing goods and services, perfect competition crushes innovation.