Because it has to be made certain that Jesus was really dead. If he was resurrected few hours later, modern Bible readers would think that he was just in a coma and he was not really dead.
The three day period is one good way to make sure, beyond a shadow of doubt, that Jesus did die and was later resurrected. The truthfulness of the Christian faith rests mainly on the resurrection. If Jesus didn’t die, he could not be resurrected. And if he was not resurrected, our faith is useless (1 Corinthians 15:14).
There are other secondary reasons why Jesus came back to life three days later. He himself predicted it (John 2:19) and Jonah’s stay inside the belly of the fish is a pre-figuring of Jesus’ burial (Matthew 12:40). I believe, however, that God providentially intended for Jesus to remain in the grave for three days because He knew that 2,000 years later, people would question the historicity of the death of Jesus.
It should be noted that Jesus didn’t really stay the full 72 hours in the grave. The Jews count their days differently than we do. Jesus was buried on a Friday and was resurrected on a Sunday. For the Jewish reckoning, Friday was first day, Saturday was second day, and Sunday was the third day.