Ah, I see the discussion is now limited to the four Imaams because you discovered that their Madhabs which are not based only on the 4 Imaams but on a host of scholars who followed them did accept Qiyaas.
Let me direct you once again in a matter you have admitted not to know too much about.
أما القياس الشرعي إذا عدم النص والإجماع فقد ذهب جمهور أئمة الصحابة، والتابعين، وجمهور الفقهاء والمتكلمين إلى أن القياس الشرعي أصل من أصول التشريع، يستدل به على الأحكام التي لم يرد بها السمع، ونقل عن أحمد: لا يستغني أحد عن القياس
As for al-Qiyaas, when there is no Nass and Ijmaa then the majority of the Imaams of the Companions (may Allaah be pleased with them), Taabi'uun, and the majority of Jurists and Mutakallimuun have said that Qiyaas is an 'Asl from the Usuul of Islamic legislation....
Imaam Ahmad said:
Everyone has a need for Qiyaas.
Imaam al-Shaafi'i discusses Qiyaas as a means to derive rulings in his book al-Umm and al-Risaalah.
I hope that helps. : )