Or, maybe it’s okay to “purge everything,” as it’s possible that Cloudflare is exaggerating the impact?
I wouldn’t say Cloudflare is exaggerating the impact per se.
But Cloudflare has millions of users with different use cases and performance requirements. Some have only a handful of pages so they can easily purge the cache case page-by-page. Some have thousands or even millions of pages that make page-by-page cashing unfeasible. Some have blogs with barely any visitors and a temporary drop in site speed lasting a few seconds has no meaningful impact. Some Cloudflare customers have critical API endpoints being used by millions of other websites: they expect millisecond response time — and such a temporary drop in performance — even for a few seconds, can be detrimental.
So you always have to contextualize any advice to your specific circumstances.
As to Cloudflare’s warning about purging all cache affecting performance, all this means is that after the cache is cleared, the next time someone visits your site, Cloudflare will have to visit your hosting server to fetch your site’s files before serving them to the visitor. This may slow down the site for under a second for this particular visitor (unless you have a really crappy hosting provider, in which case it could take a second or two extra). But after this first visit, Cloudflare will cache the assets again, and you’re back to where you were before you purged the cache.
Whether this few milliseconds-to-seconds of additional delay for the first visitor (or few visitors) to your site after purging the cache will be detrimental to your site and business or not — you are the best judge.
Good luck!