Stop complaining about discoverability, everyone that knows how to browse the web knows how to scroll. It's like worrying whether the user will know how to use a mouse when you're designing a web page. Scrolling is not something like shortcuts or tabs - you need it to move around, which means you get to know it as soon as you start your computer and after the first knowing phase it's visual clutter.
Also, I would like to ask whether users will usually even want to click on the scrollbar to move around. Unless the small number of cases where the page is long and you want to move around quickly (and if you have ever been in that case, you know that even there using the scrollbar is pretty useless because it's too sensitive - you are usually less precise when you use a scrollbar, not more), there's virtually no reason to click it. Computer screen estate is precious because not everyone is using a 27-inch display (13-inch display here), so that's a pretty big reason to hide the scrollbar.