There are many, many research and case studies [3] correlating improved website performance to improved business metrics (such as conversions).
Google Search has also signaled that the Core Web Vitals will become a ranking signal [4].
Disclosure: I work on Lighthouse and web.dev
[1] https://web.dev/how-to-measure-speed/#lab-data-vs-field-data
[2] https://web.dev/vitals/#core-web-vitals
[4] https://webmasters.googleblog.com/2020/05/evaluating-page-ex...