From the looks of the competition so far, teams have been very smart and responsible on how they use tape (if any) on their robots.
There are four small 1/2" wide strips of duct tape on our robot. We put them around the
outside of the screws on our elevator rollers, to keep the screws from backing out if the Loctite fails, or if the students forgot to use Loctite on a screw or two

. Absolutely no problems, and a much more elegant solution than trying to use some kind of flexible material and two zip ties.
It seems the fears of tape being used on robots have been greatly exaggerated, and I look forward to a continuation of this policy in future years.