I thought the following by Poythress on grammatical-historical exegesis was helpful. As I have suspected, this method is not comprehensive in its attentiveness.
I would claim that the NT authors characteristically do not aim merely at grammatical-historical exegesis of the OT. If we expect this of them, we expect something too narrow and something with too exclusively a scholarly interest. The NT authors are not scholars but church leaders. They are interested in showing how OT passages apply to the church and to the NT situation.
Positive Side of Grammatical-Historical Exegesis
(1) In writing the Bible God spoke to people in human language, in human situations, through human authors. God himself in the Bible indicates that we should pay attention to these human factors in order to understand what he is saying and doing.
(2) On a practical level, grammatical-historical exegesis serves to warn the church against being swallowed up by traditionalism, in which people merely read in a system of understanding which afterwards is read out. It alerts us to nuances in meaning that we otherwise overlook or even misread.
(3) It serves to sensitize us to the genuinely progressive character of revelation. God did not say everything all at once. We understand him better the more we appreciate the wisdom involved in the partial and preliminary character of what came earlier (Heb 1:1).
Dangers of Grammatical-Historical Exegesis
(1) If grammatical-historical exegesis pretends to pay attention to the human author alone, it distorts the nature of the human author’s intention. Whether or not they were perfectly self-conscious about it, the human authors intended that their words should be received as words of the Spirit.
(2) God’s meets us and speaks to us in power as we read the Bible. God’s power and presence must be taken into account from the beginning, just as we take into account all that characterizes a human author of any human text. We cannot, with perfect precision, analytically isolate God’s propositional content from his personal communion. To attempt to perform grammatical-historical exegesis by such an isolating procedure is impious.
(3) It is legitimate to explore the relations between what God says in all the parts of the Bible. When we perform such a synthesis, what we conclude may go beyond what we could derive from any one text in isolation. Yet it should not be in tension with the results of a narrow grammatical-historical exegesis. (Of course, sometimes because of the limitations of our knowledge we may find no way to resolve all tensions.)
(4) We are not to despise laypeople’s understanding of the Bible. We are not to reject it just because on the surface it appears to “read in” too much. Of course, laypeople may sometimes have overworked imaginations. But sometimes their conclusions may be the result of a synthesis of Bible knowledge due to the work of the Holy Spirit. Scholars cannot reject such a possibility without having achieved a profound synthetic and even practical knowledge of the Bible for themselves.
(5) When later human writers of Scripture interpret earlier parts of Scripture, they typically do so without making fine scholarly distinctions concerning the basis of their knowledge. Hence we ought not to require them to confine themselves to a narrow grammatical-historical exegesis. In many respects their interpretations may be similar to valid uses of Scripture by nonscholars today.
(6) God intends that the Bible’s words should be applied in people’s lives today. In complex personal, social and political situations, we may not always be sure what the correct applications are. But applications genuinely in accord with God’s word are part of God’s intention. Hence, in a broad sense, they are part of what God is saying to us through the Bible as a whole. God continues to speak today. When we read the Bible aware that it is God’s word, we understand that he is speaking to us now. We are constrained to obey, to rejoice in him, and to worship.