Why would the early Christians invent the story of an empty tomb? At least two factors (besides sheer mythmaking) may be the sole or contributing reason(s):
1. On page 147 of Scripting Jesus: The Gospels in RewriteL. Michael White figures that there was a sort of back and forth arms race between claims of Jesus' resurrection and skeptical opponents. The Christians began by claiming "Jesus was raised". Skeptics, White hypothesizes, responded with "You only saw a ghost!" It is notable that conservative scholar N. T. Wright, in his book Resurrection of the Son of God, points out that post-mortem appearances were normally understood in ways other than bodily resurrection. Hence, critics of Christianity might have been especially likely to reply that the Christians had "only seen a ghost". White figures that the empty tomb story originated in order to emphasize the physical nature of what the Christians were proclaiming about Jesus. They didn't simply see a ghost, they saw a resurrection, and they were sure of it because the body had gone missing. To which the Jews (or perhaps some other opponents of Christianity) responded that the disciples stole the body (see Matthew 28) to which the Christians responded that there were guards at the tomb (see Matthew 27 and 28) to which the opponents responded that the guards had fallen asleep, to which Christians responded that the guards had been bribed to say they had fallen asleep when they hadn't.
Hence, the origin of the empty tomb story as part of a propaganda war is highly plausible. It's plausible, if not highly probable, that there were propaganda wars between Christians and their detractors (Matthew makes that much clear). It's plausible, if not probable, that the Christians claiming to have seen the post-mortem Jesus would have been answered with "you only saw a ghost." And one response to such a charge would be: "We didn't see a ghost, it was really Jesus. If we had seen a ghost, the tomb wouldn't have been empty." That response would be very plausible. In fact, I'm willing to bet that someone would have made such a response whether it was true or not.
2. Pre-Christian Jewish and Pagan traditions contained stories of a hero figure whose body went missing after death. Some examples are listed below. Suffice it to say that if this was a common story to tell about a hero figure (and it was), then it is likely that the Christians would have borrowed it. Why? Because it was what was commonly expected of a prophet or Son of God or hero. Because people might naturally wind up confusing the already similar stories of Jesus with the missing body stories of other Sons of God/ancient holy prophets.
2 Kings chapter 2 records Elijah going missing and his body not being found even after being looked for for three days. If you read the second paragraph of Plutarch's Numa Pompilius you'll find out that Romulus' body was "never seen alive or dead" after Romulus disappears in a whirlwind. Other parallels can be found in my DB Skeptic article and also in Robert M. Price's book The Incredible Shrinking Son of Manin which Price demonstrates extensively that many "apotheosis" narratives like the two I've mentioned were told about other figures around the same time Christianity was born.