From an example in Mastering Small Stakes No Limit Holdem (pg. 383):
Notice that Hero [on the river] has nut hands slightly more often than bluffs. When this is the case, as long as Hero does not have more bluffs than value bets, he should bet as much as possible.
Question: Why is this the case?
When hero bets as much as possible on the river, he lays his opponent odds
xthat approach (but never touch) 50%.
Suppose shoving lays your opponent 33% odds, and the top 40% of your range are value hands. Then I can see your opponent having a psychologically hard time calling with bluff beaters that technically beat the 33% percentile of your range (this might require him to call an all in with ace high, for example).
But now suppose that shoving lays your opponent 45% odds. Then he is only rational to call with hands that beat the 45th percentile of your range, which means (at the very least) he is only rational to call with premium hands. What is the benefit of this?
In general, why should one shove on the river when your range has more than 50% value hands and less than 50% bluff hands?
EDIT: Upon reflection, a more reasonable rule of thumb seems to be as follows:
When your river range is more than 50% value, you should bet small so as to entice your opponent to call with a marginal hand.
When your river range is more than 50% bluffs, you should bet large, so as to minimize the chances that your opponent calls (betting large will force him to make the difficult decision of calling a large bet with nothing but a bluff beater).