I think mouse users don't generally suffer from this problem: by default, MacOS always shows a scrollbar in all contexts if you have a mouse plugged in to your computer.
By the way, vSphere is part of the problem. It's one of those web applications that try very hard to look like a desktop application. It doesn't use the standard HTML behavior of building a page that scrolls. It clips everything at the borders of the screen. Ironically that reduced functionality probably cost them a lot of developer time.
No it doesn't - and why would it? Any reasonable modern mouse has a scroll-wheel or touch area so you don't need to click the scrollbar.
Not only does it not show the scroll bar by default, but (not sure if this is a Chrome or Mac issue), when it does show up during a scroll operation, you have to have great reflexes to grab it with a click if you want to.