There are a lot of people dealing in absolutes here, which we should
all know is dangerous. (Frankly, the only reason to issue an absolute blanket Do Not Pick rank on a team is for a demonstrated pattern of dishonest and unethical behaviour. This is an absolute that even a Jedi would get behind.)
I echo many of the thoughts said by others in this thread. Each team should be evaluated on a case by case basis, on how their design and level of demonstrated functionality would complement your own robot and your desired elimination strategy. From my own personal experiences, I would say that most mecanum robots we've competed with have not been fit to be included on a picklist. Sometimes this is because their drivetrain makes them easy to defend against or unable to defend others. Other times it's been because the robot is just not generally very good. However, this is not an absolute. In 2010 at GTR, we were very close to picking a mecanum robot (Team 188) over a team who has never lost a regional (Team 2056), and ended up winning the event with a mecanum robot as our third alliance member (Team 1547). So it's not impossible for teams to use mecanum wheels with a great degree of success, albeit the frequency seems to be much lower. As for any talk of an inherent bias against mecanum wheels that isn't precipitated by actual robot performance, this is just dumb. The only inherent bias I've seen from teams when it comes to alliance selection is a bias against inferior robots, which is exactly what the picking process is based around.