People who track link usage use links to a tracking service which redirects to the target, or embeds tracking metadata in the URL. You could have a tracker which produces shortened links, or try to hide your tracking metadata by putting the already tracked link through a shortener, but that's all without consequence as a shortened URL looks no less suspicious than a URL with kilobytes of metadata. I suppose some trackers might try to (mis)brand themselves more positively as shorteners though.
Nothing about a shortener helps you block spam URLs - quite the contrary, they tend to be used to hide spam URLs.
The main legitimate use-case I can think of for shortened URLs are those used in advertisements or manuals, where the user might need to type it manually.