Should usability testing of a competitor’s website be a part of your usability testing routine?

I was reading up on best practices on usability testing for websites and a recommendation was that get your participants to do usability testing on your competitors website as well as that would help you better understand how they navigate sites like yours (e.g. an eCommerce site). Though I can see the merit in that, a lot of websites have different design patterns and user flows and I am not sure if there would be any real benefit in doing an usability test of the competitor website unless the site is very similar to your own site.

Has anyone done a similar exercise and has had results which show key takeaways even though the competitor site might not be a mirror image of your site. I would also love it if there are any references to published case studies or research articles.