We're only seeing part of the story. There's a lot going on under the surface of the story that we know which never gets directly discussed - things like exactly who Aslan is, or the Emperor from Beyond the Sea. Then, of course, there's the Deep Magic which requires Aslan's sacrifice.
So, while it's never spelled out in exact detail, it's likely there is some magical benefit to killing all of them.
Prophecies can be misread. While it is generally believed that all four thrones must be filled by brothers and sisters to fulfill the prophecy, that's not actually spelled out in the wording of the prophecy that we know.
"When Adam's flesh and Adam's bone/Sits at Cair Paravel in throne/The evil time will be over and done."
That Cair Paravel has four thrones suggests that four are needed, but it's not explicit. Safer, then, to eliminate ALL the possible candidates for any of those thrones in one go.
She does. In the end, when it is clear that they cannot catch the the other three, the White Witch does attempt to kill just Edmund:
"Yet it might be better," said the dwarf, "to keep this one for bargaining with."
"Yes! And have him rescued," said the Witch scornfully.
"Then," said the dwarf, "we had better do what we have to do at once."
"I would like to have done it on the Stone Table itself," said the Witch. "That is the proper place. That is where it has always been done before."
Edmund found himself being roughly forced to his feet. Then the dwarf set him with his back against a tree and bound him fast. He saw the Witch take off her outer mantle [...]
"Prepare the victim," said the Witch. And the dwarf undid Edmund's collar and folded back his shirt at the neck. Then he took Edmund's hair and pulled his head back so that he had to raise his chin. After that Edmund heard a strange noise - whizz-whizz-whizz. For a moment he couldn't think what it was. Then he realised. It was the sound of a knife being sharpened.
So it's important to read what's going on here - Edmund isn't just going to be casually killed, but ritually sacrificed. Even at this point, when she's given up on catching the others, she doesn't just turn him to stone the way she did with other complications, or have the dwarf throttle him on the spot. She has him bound, removes her mantle, sharpens her stone knife...
It's still about more than just getting rid of a complication. She is preparing for a ritual sacrifice, presumably to draw some kind of advantage. One can only imagine what sort of advantage she might have received from killing all four of the Pevensies on the Stone Table itself.