Everything has to be understood in light of the ministry of Jesus. For example, King David is a type of the ultimate Priest-King who was to arise in the Order of Melchizedek. There is much in the Psalms that points to specific details of Christ's ministry. On a purely grammatico-historical reading much in the OT the NT writers apply to Christ would be ruled out as metaphorical language for the spiritual situation of OT Israel/ Israelites alone. The early Church then drew applications for the new covenant ministry by spiritual analogy to Christ's office.
If we presuppose two stages of hermeneutical continuity between:
1) OT type & NT anti-type, and
2) Christ's royal priesthood & the Church's royal priesthood,
many important spiritual applications can be (and were) made for Church order and worship.
We should generally assume that the ancient universal practices in the Church were based on a spiritual hermeneutic we are obliged to ourselves receive and unqualified to reject. This spiritual hermeneutic is none other than the Christian Faith in operation as the Scriptures are opened.