Now on the one hand some folks might object to that question, supposing that God hasn't granted that responsibility to anyone: on this view, to ask the question is to beg the question. But denying the validity of the question doesn't really settle things. It's not a question of whether there will be a steward of Scripture. There is going to be some steward(s) or other, whether we like it or not.
Now there are at least three ways in which someone might act as steward of Scripture: as to the books that comprise it (that is, with respect to the canon), as to the meaning of it (that is, with respect to hermeneutics), and as to the words of which it consists (that is, with respect to textual criticism). I've seen more than one argument between Protestants and Catholics about the question of the canon, and I've seen more than quarrel about hermeneutics. But I can't recall seeing one that addresses the question of textual criticism.
Let's set aside the canon and hermeneutics questions for a moment. We live thousands of years after the Scripture was first written. We have a huge number of manuscripts, and many variations among them. who decides which version of the text is correct?
Well, for the Catholic there can be only one answer to this question. Scripture has been entrusted to the Church. Consequently only the Church has any valid standing for establishing the exact text of Scripture. Hence Vatican II says:
Sacred tradition and Sacred Scripture form one sacred deposit of the word of God, committed to the Church [Dei Verbum §10; emphasis added].But the Protestant has an issue here. Who decides what the text is, and what is the basis of the authority to make that decision? I don't know of any answer that they can make to this that doesn't boil down eventually to subjectivism. Hopefully they would say that "the church" must do this, but that demands that we know what is meant by "the church". If by this they mean "my denomination," that's certainly a better answer than others that might be given. But it's hardly one that can stand historical scrutiny, since (obviously) no Protestant denomination existed before the sixteenth century.