Obviously something on the field will be happening fast enough (and/or often enough) that human judges would have a hard time. This could be anything moving on the field: field elements, game pieces, or even robots.
Whatever is happening that needs to be counted, it seems like the timing of the counting is critical. Maybe the match time will not count continuously, or maybe an event on the field must take place within a certain time. eg. If there was a plate on the floor in front of the feeder stations last year connected to a ROLLER LIMIT SWITCH and as soon as you backed away from the plate a timer would start and you would have to place the tube (detected by a PHOTOTRANSISTOR) within a certain amount of time or it would be invalid. The VERY HIGH SPEED COUNTER could be part of the timing mechanism or could keep track of the scores (it seems like the scoring will be faster than hanging tubes).
I also really like the idea someone posted a while ago about the counter being used in the finale when a bunch of mechanisms fire at once.
Although this is even more conjecture than the rest of my post, at the beginning of this thread everyone was talking about the photogates detecting "breaking a plane" and the only time I ever hear "did the ball break the plane" is while watching a football game. also: in a football game, the clock stops for all kinds of stuff, something that a VERY HIGH SPEED COUNTER could be used for.
Even if its not football (unlikely) the number (10-12 per field someone calculated) is a LOT. Even in Breakaway, there were only two goals per team, so unless there are bunch of goals worth different points (imagining aim high + ski ball) they could plan on lining up the photogates in areas to make "end zones".
I would LOVE a mixture of Aim High and Ski Ball.

The programmers would have fun.
edit: flying ski-ball game could use all kinds of balls (even tennis) and would explain the extra polycarb if the field was going to be encased for safety