I do not know much about Abubakr Ahmad Bayhaqi than the fact that he used to collect Hadiths. However, regarding the Sunni schools of fiqh, you should understand few things.
These schools do not exist to exert their opinions as truth to everyone. Rather, they exist to make it easy for a learner to get closer to truth. Be it the Madh'hab of Shafi'i, Malik, Ahmad or Abu Hanifah.
It is true that during the time of these four Imams, there were people who were equally knowledgeable and also greater in knowledge than them. These Imams of the past made efforts to learn and teach and some of them had Madhahibs that remained established.
Why did these four schools survive? Because, they had students who to serve them and take care of the knowledge that the Imams left. They were hardworking who made sure their work and the heritage of knowledge was preserved. However, not all the Imams had similar students. There were Imams more knowledgeable during that time, however they did not have students who took care of the knowledge or tried to preserve it. There were no one to preserve their rulings, views and opinions. Hence, their madhahib did not get established. This is the reason why the four schools remained and became established while others got lost in time.
During the time of Imam Abu Hanifah (Rahimahullah), there were scholars equal to him in knowledge and greater than him in Qur'an and Sunnah and Arabic Language. However, Imam Abu Hanifah had disciples and followers and students dedicated to preserving his heritage such as Zufr, or Abu Yusuf or Muhammad ibn Al-Hassan.
Similarly, in the time of Imam Malik (Rahimahullah), there were scholars equal and greater than him in knowledge and virtue. For example, Layth ibn Saad (rahimahullah), the great scholar of Egypt and people used to say Layth ibn Saad had greater knowledge than Imam Malik. And also, Ibn Abi Dhib (rahimahullah) of Al-Madinah. These scholars had knowledge either equal to Malik or more. However, they did not have students who took care of their heritage of knowledge like Maalik.
Moreover, Scholars say that the intention and sincerity of a scholar to Allah has effect upon how much his knowledge benefits the creation. Allahu A'lam.
I hope that answers your question (at least partly).
My answer is based upon this piece of lecture by Shaykh Saleh al Luhaydaan.