"Then the king, the governor, Bernice, and all the others got up, and after leaving they said to each other, “This man has not done anything for which he should die or be put in prison.” And Agrippa said to Festus, “This man could have been released if he had not appealed to the Emperor.”"

(Acts 26.30-32 GNB)

If Paul had not appealed to the Emperor, he might have been released. (Not so sure about that.) And if he was released, he might still be continuing his missions and he may write more about the faith.

But what if his mission was to go to Rome and die there?

A mission sometimes ends "badly" for those who go, but that mission sparks something that will, years later, starts a fire. True in Paul's case and true in many cases thereafter.

Only God knows what the real mission is.

Related:
He knows better
Mission and me