The search neutrality debate is about whether search engines should or should not be allowed to uprank certain results among the organic content matching a query. This debate is related to that of network neutrality, which focuses on whether all bytes being transmitted through the Internet should be treated equally. In a recent paper, we have formulated a model that formalizes this question and characterized an optimal ranking policy for a search engine. The model relies on the trade-off between short-term revenues, captured by the benefits of highly-paying results, and long-term revenues which can increase by providing users with more relevant results to minimize churn. In this article, we apply that model to investigate the relations between search neutrality and innovation. We illustrate through a simple setting and computer simulations that a revenue-maximizing search engine may indeed deter innovation at the content level. Our simple setting obviously simplifies reality, but this has the advantage of providing better insights on how optimization by some actors impacts other actors.