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.

Maybe, but having random "accurate" behavior in a program is generally worse than being incorrect all of the time.