You are the one blinding yourself with Shanks hate
It doesn't matter for me because it won't happen anyway knowing Oda's style, just telling you now if BB doesn't shit on Shanks then don't complain.
How defeating Bb on Marineford would force Marines to fight more?
Sengoku and Marines let WB and BB kill each other because thats their usual tactics. As Sengoku also expected Croco to attack WB and was surprised when Croco helped WB.
Shanks could defeat BB first (assuming he could) and Marines would welcome it, then end the war later, no difference.
Also no excuse for what happened later, Shanks still sit and watch Bb doing tons of things during that 2 years time skip, watch him become Yonko.