Is Google harming my site speed by showing my 301 old URLs?

I need your opinion on an assumption I'm building up for an argument.

Assuming I changed several URLs from my website with 301 redirects, and Google is stubborn and taking their time to change them in the SERPs. (i.e: the pages still rank properly but the pages shown are redirects to the new version)

Does this create latency to my site because of the extra HTTP request of a redirect? Can I assume that GOOGLE is (ironically) creating latency and therefore making my site slower which is something they advocate against?

What are your thoughts?

Yes 301 slow the request down... usually by a fraction of a second on most servers. Make sure you have proper canonical URLs on the pages to the new URL and make sure you updated all the navigation and other links on your website to the new URL. This also includes any sitemap files and RSS feeds.

If you don't update everything then Google rediscovers the old links and gets confused.

Other than that it often takes a month or more for Google to finish up the switch. If you have a lot of pages on your site then expect it to take a bit longer for google to recrawl everything. You can look at your Google cache dates to see if google has updated its copy of the content... look for the new URLs in the canonical or navigation if nothing else has changed.