Consider the logarithm. In almost any interval, rounding down will be more accurate than rounding up the majority of the time -- so random rounding will bias you away from an accurate result. Random rounding can be a good idea, but it's not always a good idea. Random rounding is an okay default, but having fine-grain control over rounding direction is vastly superior to always sticking to the default.

For another example, interval arithmetic is a really cool approach to keeping an eye on your accuracy. There, you want to round your upper bounds up, and round your lower bounds down.