C9 couldn't have rushed inhib because by the time they got baron the entire TSM team had respawned.
And Elder was the only objective available if they wanted to speed up the game.
But I agree the whole sequence was just a series of terrible call by C9 that let the "weaker" (in that game) win and thus win the entire series
They should have contested Elder, but not go for a 50/50 fight at Elder, they should have kept the 4/1 push on the side with Baron buff and let Ekko TP in only if they could have had a favourable/winnable teamfight
Also the base race with only two people alive was idiotic, in that situation recall and defend that bot lane to stall until your mates respawn and can protect the remaining members with the buff ( TSM got better position at Elder because even after getting Baron C9 sent no one clearing a pair of minion waves bot to depush/counterpush It back, and so TSM got a freeway to close the game and series).
If It was a Korean team in C9 situation, TSM would have never won that game