I have always (since my student days 30 years ago) just mentioned my destination on first contact. When speaking to a controller for a specific phase of flight, I have regularly mentioned a deviation from straight line. For example, on a flight west into the mountains from Denver, I would let them know which pass I intended to cross. Or, approaching a restricted area later enroute, I would tell ATC I was talking to then that I would pass east of it.
It is being polite. They are nice enough to provide advisories. The least I could do is let them know what I was doing--- in their airspace. But I doubt a controller in Kansas City cares what I am planning to do hours later nearing Chicago, so no, no "via" for me.