You give me one good reason why the paper should be torn up? it is a visual compromise, anytime you ask someone to write anything down that is a compromise if not you would just guess the word from the subjects head.
I'll assume that you are performing the demonstration to more than one person. It makes sense that if a single spectator out of many is thinking of a word, they would let the others (or at least those immediately around them) 'in on' the effect. A way of doing this is having this written down and shown around - "Whatever you do, don't say it out loud, just take this pen and I've got my business card here...".
Another explanation you can give is that since everything is going to take place between your minds, it is easy for the spectator to lie purely just to make you look good, or conversely, embarrass you. So to make sure they won't change their mind or anything have them write it down. There are plenty of rational reasons for billet work to take place and I don't think it should be seen as compromise.
So why should the paper be torn up? One reason I have used in the past is that after the first reasoning I gave for the word to be written in the first place (to show other spectators) I take back the paper and pen (with a sense of unimportance), look to the people around the spectators and ask "So did everyone see the word? Yes? Okay then we'll get rid of this" Execute CT. With a sense that 'we dont need this anymore'. That is one string of logic that I have followed, since you asked, and I think the paper is torn with good reason. After all, you are simply destroying the physical evidence of the word, leaving the rest of the effect to happen in their mind. And since it is with a group of people you can incorporate that into your presentation, talking about how the thoughts of a crowd being stronger than that of a single person [insert cheesy trade show/cliche motivational message here]
Just because something is old and overused does not mean it is good, it means it is relied upon as tool. I agree it is the ambiance the performer portrays that makes the situation believable but to anyone with any logic it doesn't make sense.
...Unless you give them reason for it to make sense. Yes, the CT is old and yes, I agree it is possibly a little overused but I do believe that it is good. It is versatile, deceptive and I have personally used it hundreds, possibly thousands of times and fried people...logical people. I don't think it should be used without presentation (I think you understand this), but I think that it should be justified through that presentation.
There are far better moves that are more believable and less 'fishy' to the lay (not talking about impression devices), I think the move it self is genius (for the time period it was invented) But still lacks reasoning.
I agree that there are other - better - moves out there. I currently use a switch more than a tear but that is just personal preference. I don't understand, however, how a move can be 'believable' or not, it is the effect and the demonstration that is measure on believability. Remember the CT is a tool.
You say the move is great but lacks reasoning? It doesn't have reasoning, you have to give it reasoning. Think about it, be creative.