WP only needs to modify itself if it updates itself. You can manage updates yourself with a git or even a CI workflow if you want to. These work the same way for WP as they do for a static blog codebase.

Or, you can keep folders locked down until it’s time to update, then unlock and let it update itself, then re-lock the permissions. This can be done manually or with a job scheduler.

WP needs a caching strategy for performance but so do static blog generators. The static copy is the cache, and rebuilding it is the cache purge.

Edit to add: Wordpress is so popular there are dedicated hosting companies, which makes all this stuff super easy. I managed WP myself for years; now I just have an account at WP Engine and they handle all this stuff for me.