Bradbury requires a setting in the future because the setting includes technology that is more advanced than when he wrote the story. In the story, the family house is automated. Bradbury supposed a time when two things would be possible. One is that technology would be so advanced that most daily tasks (cooking, cleaning, scheduling, even remembering) would be done electronically and mechanically. In other words, technology would make things so convenient that people would essentially be taken care of by machines. The other thing that such an advanced technology would make possible is more powerful weapons.
As the age of technology increases, the means for convenience as well as the means for destruction both increase because both developments are based upon technological advances. The implication (the lesson) is that if people allow their technology to take over their lives, they are in danger of destroying themselves. By relying too much on machines to do everything for them, people become less human, less active, and less inclined to think for themselves (especially if machines do the scheduling and remembering for them):
It repeated the date three times for memory's sake. "Today is Mr. Featherstone's birthday. Today is the anniversary of Tilita's marriage. Insurance is payable, as are the water, gas, and light bills."
If people are less inclined to think and do for themselves, and if this occurs in a future age when weapons become supremely destructive, then we a have a future scenario where/when people are thoughtless and even more capable of destroying each other. This is a cautionary tale about technology. (Note that Bradbury was personally in favor of technology but simply supported a responsible and thoughtful program for it.)