It has been well said that mankind's greatest enemy is death. Whoever would be the Savior of all mankind must then, of necessity, conquer mankind's greatest enemy. Had Jesus merely died and returned to Heaven without overcoming death, then man's greatest enemy would remain unconquered. As it is, we can ask along with the apostle Paul, "Where, O Death, is your sting?" (1 Corinthians 15:55) Death's sting has been thoroughly defeated. So, the first reason is that death had to be conquered.
Secondly, the resurrection proves that Jesus is not merely a great, albeit misunderstood, teacher, nor is He merely a prophet or a narcissist. No, the resurrection proves that Jesus is divine, as Paul states:
Paul, a servant of Christ Jesus, called to be an apostle, set apart
for the gospel of God, 2 which he promised beforehand through his
prophets in the holy Scriptures, 3 concerning his Son, who was
descended from David according to the flesh 4 and was declared to
be the Son of God in power according to the Spirit of holiness by his
resurrection from the dead, Jesus Christ our Lord. Romans 1:1-4 ESV
Indeed, it was and is the resurrection of Jesus that brings credibility to His otherwise incredible claims. If there were no resurrection, Christianity would be nothing. Indeed, Paul also says that very thing:
And if Christ has not been raised, your faith is futile and you are
still in your sins. 18 Then those also who have fallen asleep in
Christ have perished. 19 If in Christ we have hope in this life only,
we are of all people most to be pitied. 1 Corinthians 15:17-19 ESV
It is also the resurrection of Christ that gives us the hope of resurrection for ourselves.
So, three significant reasons are 1) to conquer death, mankind's greatest enemy, 2) to prove His Divinity, and 3) to give followers of Jesus the hope of resurrection.