Why did Al-Bukhari and Muslim not narrate some shared Hadiths, and are Hadiths not narrated by the two Shaykhs considered unreliable, even if they are well-known?

Al-Bukhari and Muslim did not undertake to mention all authentic hadiths in their two books; rather, they left out many of them. The five books of hadith did not miss much of the authentic hadiths, and Al-Hakim indeed supplemented them with many hadiths that met their criteria, and there are other hadiths that are authentic but did not meet their criteria.