Google cares about the speed of your site
If your client cares about their ranking in search results then page speed is important, per Google. Anecdotally, we've noticed improved results with client projects when page speeds have been improved.
To check your site's page speed, go to Google's PageSpeed Insights and enter the URL for the site. The site landing page (typically the front page) is what's relevant. The site should score a 90 or higher. If your score is high and you haven't spent time optimizing the site, you likely can push it higher.
A score of 100 is not always achievable, but try to get as close to it as possible.