Thanos: When we faced extinction I offered a solution
Dr. Stephen Strange: Genocide?
Thanos: But random, dispassion is fair for rich and poor a like. They called me a mad man. What I predict came unannounced.
Dr. Stephen Strange: Congratulations, you're a prophet
Thanos: I'm a survivor
Dr. Stephen Strange: Who wants to murder trillions
Thanos: With all the six stones I can simply snap my fingers, they will all cease to exist. I call that... mercy.
Dr. Stephen Strange: Then what?
Thanos: finally rest, watch the sunrise on an ungrateful universe. The hardest choices require the strongest will.
The key conversation and relevant parts bolded above.
Thanos wants this to be completely random and dispassionate, and he also wants it to be snap-of-the-fingers immediate.
Aside from not being very interesting as a movie plot point, simply affecting people's fertility wouldn't stop the Avengers. Striking people with infertility also isn't truly random - rich people would end up buying/stealing/making legal the practice of taking babies from poor people.
Also, Thanos is a egotistical, delusional maniac - snapping his fingers and having no visible effects for several years doesn't make him look very powerful.