[sgreco]

The major reasons have been stated, but the biggest for me is the redundancy in gear ratio of having a big wheel. Gearing down then using a big wheel is redundant. The wheel size is part of your gear ratio. If you have a 2 stage reduction gearing down 12:1 with an 8 inch wheel, you could achieve the same ratio with one stage 6:1 and a 4 inch wheel. The weight savings add up, lighter wheel, less reduction, therefore fewer gears etc...You will also get better acceleration (relative to the gear ratio) with a smaller wheel because, in a general comparison, smaller wheels have a smaller moment of inertia.

(Big wheels do have some advantages in tackling rough terrain, but we don't see that too much in FIRST).