Are there any English idioms to describe “futile benevolence?”

There is the proverb "no good deed goes unpunished."

There is also the expression 'casting pearls before swine'.

There is also biting the hand that feeds you

to treat someone badly who has helped you in some way

This is more a description of the recipient of the benevolence than the purveyor.

I have heard the expression "hand-to-mouth approach" used in reference to Western efforts to feed Third World poor, with the implied criticism that the approach is ultimately unproductive (I hasten to add that I don't mean to imply agreement with this, only to report on the usage).

From the episode you are describing from Chinese history a better English equivalent may be "misplaced chivalry".

In the Bible

1 Samuel 24 - David Sparing Saul's Life.

King Saul had cultivated a jealousy against his general David. Soon that jealousy becomes enmity, from which David had to flee because Saul was after his life. So David became a rebel warlord, with Saul's constant harassment on his life. One day Saul took a rest in a cave, where David and his men chanced upon him sleeping.

David's men hankered after him to have Saul killed. David refused. David even regretted in anguish having cut off a piece of Saul's garment (I guess to prove to Saul that David meant Saul no harm) while he was asleep.

When Saul awoke, David persuaded Saul to repent of his pursuit of David's life. Where Saul expressed remorse with David bowing before Saul his father-in-law and former boss, setting him free. But Saul did not stop pursuing David's life.

Within communities where there is a strong reliance on the Bible for ethical guidance, an honest politician could convince him/herself to spare Saul's life. An honest politician who refuses to smear his/her opponent with negative campaigning even when possessing a piece of information that would end the opponent's political career. While the opponent uses all means available to destroy the honest politician's reputation.

They (the honest politician) would say "As David spared Saul's life ....".

They could also probably say, "As in 1 Samuel 24, I will be rewarded."

One idiomatic expression in English that typically involves turning an ostensible virtue into a vice (or a source of harm) through excessive or injudicious exercise of it is "to a fault."

The most common specific phrase used in connection with "to a fault" is "generous to a fault," which means being so generous that the generous person ends up harming the beneficiary or others or himself/herself, or not setting a good example of how to behave properly.

But there is no reason you couldn't say that someone is "benevolent to a fault" or "kind-hearted to a fault" or "chivalrous to a fault" or "gallant to a fault" or "sportsmanlike to a fault" or even "principled to a fault."

Here is the entry for "to a fault" in Christine Ammer, The American Heritage Dictionary of Idioms, second edition (2013):

to a fault Excessively, extremely, as in He was generous to a fault. This phrase, always qualifying an adjective, has been soused since the mid-1700s. Indeed, Oliver Goldsmith had this precise usage in The Life of Richard Nash (1762).