It's no different to 'clear the whole cache every time I change any content and store it all in memcached' - you're just substituting 'file-system' for 'memcached'.
Of course - SSG do solve another problem - that of needing complex software running on your server - you can run SSGs locally or on a centralized server - but that's not what is being discussed here.
There's no reason why the SSG needs to rebuild the entire site if you've only changed one thing.
On the other hand, if you start with a SSG, your initial state is that every page is cached and works, and you have to think carefully of adding some kind of pagination mechanism.
As the quote goes, "There are only two hard problems in Computer Science: cache invalidation and naming things." The big benefit of a SSG is that you 'solved' the cache problem, and will immediately be aware of issues there.