It seems obvious to us that scriptural passages from the Tanakh should be cited liberally in the prayers of the synagogue. The Tanakh is replete with examples of prayer and praying.
There is a short book of collected essays on the subject that calls the process of using biblical verses in Jewish prayer "scripturalization". We call it citing and interspersing Tanakh passages into prayers.
Just to see how the verses of scripture are interspersed in the prayers more graphically for the Shaharit service (morning prayers) we put the references into a spread sheet.
Our columns are prayer name, page in Koren/Sacks Siddur, biblical (or occasional Talmudic) source, and comment (on whether or not it uses a full chapter).
In the cases listed - there is little to no distinction or demarcation between the rabbinic prayers and the earlier biblical passages. Some uses of scripture are obvious and stand out and some intermingling of verses is seamless and would not be recognized by the average reader without a reference to point it out.
The choice of what verses and chapters to use was not accidental. Accordingly they analysis of the materials tells us a great deal about the theology of the framers of the prayer services.
We also wanted to have handy a catalog of the explicit annual Torah and Prophetic readings in the synagogue. So we culled this table and put it out there as well. It is based on a yearly cycle that most Orthodox synagogues employ. Keep in mind that the triennial cycle of Torah readings was practiced until the middle ages.
The processes by which the prophetic materials were selected appear for many instances to be based on a straightforward thematic coherence with the Torah portion for the week. Beyond that, where selection is not based on obvious associative principles, by examining the selections we can learn something about the theological agenda of the later synagogue leaders who canonized the haftarot.