That paper had some serious methodological issues and the results have been shown to be misunderstood/incorrect in the majority of cases. In fact, in many cases structured outputs have shown to improve the quality of the results from an LLM (at least in terms of evaluation performance). The team at behind the Outlines library released a response the covers the issues in details and provides more information about structured outputs [0].

0. https://blog.dottxt.ai/say-what-you-mean.html