I haven't tried jekyll so I can't really comment on it. Im guessing it only generates the changed files everytime you push to git, no? As for your question, it depends on other factors too. Who are your users, what is your web app, is it an ecommerce site? Is the jekyll/git/CI workflow easier than just pressing a few buttons on the screen everyday? Those are the questions you should ask. jekyll might be obvious for us devs but we are a minority compared to the rest of the population.

Take HN as an example. This can't be done as a static site.

Or a simple guestbook or hit counter.

Where the lines may blur is JS front end talking to a BaaS... This may make it possible to glue up impressive sites using just HTML and JS with no custom backend requirement.