Genetic Drives
One must presume that the behavior is genetically driven.
Explaining Things Through Evolution
Whenever a question of the form "Why does this mating strategy exist?" the answer must always be because strategies with small changes will produce fewer copies of the genes that produce them in the next generation.
When explaining such things, the usual thing is to explain it in terms of what the organism's genes know and want. This is as old as the book "The Selfish Gene" by <PERSON>. It should be understood to be a metaphor, not actual anthropomorphism. I don't actually think that genes have knowledge and desire. They behave as though they do, since when they behave selfishly they get copied more.
Known Cases in Other Animals
Some quick examples.
If a male cat (house cat, leopard, tiger, lion, etc.) encounters a kitten under a certain age, he will kill it. He won't eat the body, just bite it until it is dead. This is because male cats are nomadic. A kitten under that age is unlikely to be his kitten. And if mother cat loses her kitten, she will be receptive to mating much sooner. So Mister Cat will have a receptive female, and remove rivals from the gene pool. As a genetic strategy, if he does not kill that kitten, the rival genes stay around, and Mother Cat stays unreceptive until the kitten is weaned. Months at least, by which time he likely has wandered away.
Males that are "good dads" to other male's kittens get erased from the gene pool.
From the standpoint of <PERSON>, it is ALSO a successful strategy. Not for her, but for the part of her potential genetic descendants that will be male. That is, her male offspring will be more successful if they do this also. So her genetics find it an attractive thing for a male to do this. She may be very upset that she has lost her kitten. She might even attack the male, scratching the heck out of him. Then she will go sulk for a day. Then she will come back and mate with him.
Because it is a genetically successful strategy, kitten-breath is a turn-on for female cats.
Consider chimps. A young male chimp must attract a mate. One thing he can do to be considered attractive is to show he is a good father. 376
So young bachelor chimps will pester mothers with babies to be allowed to babysit. And they will do it in a way to be apparent to young females, to be seen caring for a baby. The problem is, a happy baby chimp will stay quiet and often go to sleep. A sleeping baby is not going to attract any attention.
So young bachelor chimp will pinch the baby to make it cry. Then he will make a big show of comforting the baby. The females will watch and judge his efforts. They will do this on their way to judging him a suitable mate.
The thing is, it works. It works even when he gets caught pinching the baby. To a female chimp, a male who creates a big show of comforting a baby, even when he mistreats it, is a male with a strategy to attract females. If his genes include this, then his male offspring will do the same. So her genes, which are interested in getting male genes that will be successful, will find this male attractive.
Because it is a successful genetic strategy, an abusive and showy male is attractive to a female chimp. (And consider, if you dare, the huge number of stories of how step-children get treated.)
The Beepiper Case
So finally, let's turn to our queen beepiper permitting drones to mate with her offspring. She has determined through the usual process that they are suitable to mate with her. Presumably they are fresh, not the fathers of her offspring. So they are suitable mates for her offspring.
(There might be some interesting drama here over keeping them fresh. Perhaps after about the time it takes for a newborn beepiper to reach adulthood, male drones become unattractive. That might be the life-expectancy of a male drone. Slam the door on them before they get a chance to mate with their own daughters.)
So her genes know that these mates are going to provide good genetic material for her offspring, and therefore will be good for making copies of her genes. Even if her offspring turn out to be rivals. Her genes will override any thoughts of her own well being. She will have drives to do things that are good for her genes regardless of how bad that turns out to be for her.
Genetically, her offspring have 50% overlap with her. So something that produces an increase of chance of reproduction for one of her offspring that has less than 50% chance of killing her, will be genetically attractive. 335