There are two exceptions:
• I still see service-specific short URLs, e.g. goo.gl, nyti.ms, etc. Because these can only be created by the service in question, they don't introduce security/privacy concerns.
• When a URL shortener is used to create a sort of vanity link to e.g. a Google doc. (OP's service could be useful for these!)
Outside of those times... why would you use a URL shortener? When are you limited by number of characters?