I personally think that after Guilliman pretty much silenced all the other astartes with power (especially the other primarchs like Dorn) he was pretty much the only power in the council that really meant anything. After his "fatal injury" by Fulgrim, I believe that the astartes didn't really have anyone with that much influence to make it into the council. Therefore, ending the dynasty of astartes influence at that level.
I think you've hit the nail of the head there. One of the main reasons for the Codex Astartes reforms in the first place was to remove the sheer amount of power and influence Astartes commanders/Primarchs had. It seems that he trusted himself with such power as he sat on the council of High Lords (IIRC), but after himself he percieved that no other Astartes or Primarchs could be trusted with such power.
Another reason could possibly be the inherent purpose of the Adeptus Astartes. They are the protectors of humanity, not their rulers. They do not administer or lord over humanity, they use their considerable power and influence solely to protect humanity from the countless threats that they face in the harsh reality of the forty-first millennium. The Emperor consistently stated that the Imperium was not his (and as a result not his logical successors; Primarchs/Astartes), but belonged equally to every man. I see this as a logical reason as to why Astartes (or at least representatives of the entire Astartes brotherhood) don't sit on the council of High Lords.