Isn`t it also possible that said daemon prince gained ascendancy with the aid of a minor chaos power?
Not necessarily. A LoC is naturally more powerful, it knows authority and would not overlook the chance to gain more. Blue horrors are described as argumentive and spiteful, but the scribes obviously have the wit to see the task through. Bear in mind, Heralds themselves ARE lesser daemons technically. Would you consider Skulltaker or Epidemius to be dim?
A focused mindset does not mean that they cannot think.