The appeal of sending a letter isn't to avoid human contact, it's to avoid the time suck of aggravation and frustration that these dark pattern schmucks throw in the way. If it were _possible_ to tell someone on the other end of the phone to fuck off, everyone would do it. You'll get an IVR, multiple HUCAs, and if you're lucky, someone who confidently assures you that your service is now cancelled; until you go away for a month and realize you're still being billed.
The letter is both a paper trail and a recognition that it's the fastest and sanest way to get a problem resolved. That we have to resort to an anachronism is a consequence of the fucked nature of these parasitic companies and the total power imbalance between them and consumers, not a failure of will!