I do not think it is inappropriate to use the word take-off on the PA. It is as likely to be misinterpreted by us both, remember its one of the pilots saying it, as it would be to just line up without a clearance. There are no call signs given in the PA, the other pilot can't hear it. It is totally out of context.
Hmm, if you seriously believe that SloppyJoe you could be the next Tenerife! I understand what the OP's point. I wholeheartedly agree and endorse that the words "take off" on the FD should only ever be spoken as readback to the ATC clearance.