All of the information from this answer comes from this article from Orthodox Union. Please refer to this article for further reading.
The bimah, or the platform from which the Torah is read, is placed on a raised platform for several reasons (you might be wondering where I'm going with this, but stay with me):
An "aliyah" literally means an "ascent", and so when someone receives an aliyah (an ascent) to read the Torah he must literally ascend to where the Torah scroll is placed. Also, since the Torah was given on Har Sinai, which was held above Bnei Yisrael during Mattan Torah, the bimah is raised to commemorate this.
There is also Scriptural support for having the bimah on a raised platform. When Ezra read the Torah to the people, he stood on a platform (Nehemiah 8:4). Additionally, during the Hakhel celebration, the King would sit above the people as he read the Torah aloud. The bimah is also likened to the Altar, which was, generally speaking, a high platform. (The reason the bimah is placed in the middle of the synagogue is so all the congregants can see the Torah.)
The amud, on the other hand, is the lectern from which the chazzan prays and leads the congregation. The amud is generally placed at the front of the synagogue by the Aron HaKodesh, and is unique to the Ashkenazi custom. The Sephardi custom is that the chazzan davens and the Torah is read from the same place, the bimah.
There is a Polish custom to make the floor in front of the amud slightly lower than the rest of the floor, to fulfill the verse "From the depths I called You, Hashem" (Psalms 130:1). This is derived from the Talmud (Brachos 10b), which states that one should not daven from a high place, but rather from a low place, citing the above verse from Psalm 130.
The Shulchan Aruch (O.C 90:1) also states that one should not daven from a high place. (See also Mechaber, Hilchos Tefillah, 90:1.) And the Mishnah Berurah (90:3) explains that the reason is because it is haughty to daven from a high place, and again, cites the verse from Psalm 130 above.
So it is clear that the Ashkenazi opinion is that it is forbidden to daven from the bimah because of its high place on a raised platform. Please see the linked article for opinions that it is permitted, as well as the Sephardi opinion, etc. My job here was just to summarize the relevant contents of the article, for the convenience of others.