I would always suggest using some kind of caching plugin for WordPress sites (such as WP Super Cache – https://www.ads-software.com/plugins/wp-super-cache/, or W3 Total Cache – https://www.ads-software.com/plugins/w3-total-cache/). You may even want to look into some kind of CDN service, such as Cloudflare.
Effectively, the CC Child Pages plugin is adding another loop to the page … and if you do not create custom excerpts for each page, it will retrieve the content of each page to create an excerpt on the fly … all of which will inevitably lead to an increase in processing time, and the more pages it needs to process the longer the delay.
Caching the pages would reduce the impact of this.
The plugin is written to behave nicely with other plugins that compress CSS and JavaScript files, although I doubt that the small amount of CSS code added by this plugin would cause much of an impact in terms of speed … it may be worth using a plugin that will compress all CSS files into a single optimised one.
