I took your advice and tried this out because you seem so adamant and I was surprised that not only was it easy but "cancel my plan" is actually a voice activated option! First I said "billing" and then "cancel my plan" was the last option under billing. I then had a customer service rep that transfered me to a person who could ultimately cancel my account. I really don't see any issue here at all. I literally had a live person on the phone in under 2 minutes from the time I dialed.
I invite anyone to try it as well. You will see that it takes under 2 minutes and that is at 7PM EST when other service numbers are usually "experiencing a high volume of calls."