In both the Haram Masaajid in Makkah and Medina, before the janaaza after each fard, I see people rushing to squeeze their sunnah (post fard) before the janaaza even skipping the dhikr. Is there a valid reason for this?

Ustadh AbdulAziz al-Haqqan

the rawatib may be delayed and prayed after the janazah, its time lasting until the time of that prayer ends. So, Allah knows best.