In fact the opposite is true. The most viable sperm are tremendously coddled and nurtured by processes and systems within the female reproductive tract right up to the moment the egg is fertilized. According to a recent article in Human Reproduction Update journal "human sperm are deposited into the anterior vagina, where, to avoid vaginal acid and immune responses, they quickly contact cervical mucus and enter the cervix. Cervical mucus filters out sperm with poor morphology and motility and as such only a minority of ejaculated sperm actually enter the cervix." This means that special mucous in the female system beginning at the cervix protects the best sperm from attack by the woman's immune system. What's more, there are special biochemical factors that actually improve the swimming ability of the finest sperm. Later, other chemical signals capacitate select sperm so they have the ability to penetrate the egg. Muscle contractions and other processes help the sperm along within the female. In addition, there are nutrients and storage places further along the female's reproductive tract in the fallopian tubes. Then there are heat and chemical guidance systems that help the sperm find the egg, and also energize it even more. So contrary to your hypothesis, the female does everything possible to help and encourage the sperm, and keep them alive for up to three or four days so that her egg can be fertilized. This is why it's a good idea to wear a condom.
It should be noted, however, that apart from the few thousand sperm that are selected and protected by the female, as you suggest, all the other billions of sperm are attacked and destroyed very quickly by the female's immune system within a few hours. A hypothesis for how this works can be seen in this article on reproduction from the Weizmann Institute in Israel.