Abu Bakr was made the caliph purely on the grounds of tribal superiority of the Quraysh and other tribal practices like age equals greater authority and so on. The only non-tribal point given at the Saqifa by Umar in the favour of Abu Bakr was his kinship with the Prophet (saww), which of course Bani Hashim had the much greater right to.
DD, I would love to hear out your "rational" solution to the issue of the successorship to the Prophet of Allah, if you do not mind.
Dude, you cannot have a solution to something that happened 1400 years ago, though some people spend their whole lives mentally in saqifa.