Using a CDN to serve static HTML pages?

I'm planning to use a CDN to serve static HTML pages.

I thought it would be a good idea, because the website would load much faster and should therefore increase the SEO score.

Though recently, I read somewhere that a website which uses shared hosting takes a hit on the SEO score.
The CDN I use also shares the same IP addresses with other hosts that also serve their content.

Would this have a negative impact on the SEO score?
Should I go forward with this?

The CDN also serves as a proxy and access point to the web application in this case. The CDN must be able to cache frontend static material (HTML, CSS, and JavaScript) while bypassing dynamic content (API Calls) to the origin for this to function.