The Christian acceptance of the deuterocanonical books was logical because the deuterocanonicals were also included in the Septuagint, the Greek edition of the Old Testament which the apostles used to evangelize the world. Two thirds of the Old Testament quotations in the New are from the Septuagint. Yet the apostles nowhere told their converts to avoid seven books of it. Like the Jews all over the world who used the Septuagint, the early Christians accepted the books they found in it. They knew that the apostles would not mislead them and endanger their souls by putting false scriptures in their hands -- especially without warning them against them.
But the apostles did not merely place the deuterocanonicals in the hands of their converts as part of the Septuagint. They regularly referred to the deuterocanonicals in their writings. For example, Hebrews 11 encourages us to emulate the heroes of the Old Testament and in the Old Testament "Women received their dead by resurrection. Some were tortured, refusing to accept release, that they might rise again to a better life" (Heb. 11:35).
There are a couple of examples of women receiving back their dead by resurrection in the Protestant Old Testament. You can find Elijah raising the son of the widow of Zarepheth in 1 Kings 17, and you can find his successor Elisha raising the son of the Shunammite woman in 2 Kings 4, but one thing you can never find -- anywhere in the Protestant Old Testament, from front to back, from Genesis to Malachi -- is someone being tortured and refusing to accept release for the sake of a better resurrection. If you want to find that, you have to look in the Catholic Old Testament -- in the deuterocanonical books Martin Luther cut out of his Bible.
So if the apostles used the Septuagint, and regularly referred to it, why should we?