I could be mistaken, but it is never explicitly stated that he wasn't chosen for B4.
As I recall, Major Krantz was simply in charge of the final stages of construction, and may have been relieved of command once the station was operational and everything was running smoothly.
On the other side, having Sinclair in charge of Babylon 4 may not have been a concern for the Minbari. On the one hand, it was sooner after the war, and Delenn may not have been able to convince enough people on the Minbari side to support Sinclair.
However, what I believe is that since B4 was basically paid for by Earth, they got final say so over who would be running it. The Minbari could not have insisted on anyone as commander. Once it vanished, all the materials were gone, and Earth couldn't afford to build another one. In swoop the Minbari offering the materials for for the station only if they get a say so on who runs the place, and of course they want their buddy Sinclair.
If he had taken B4 and vanished with it, he wouldn't have been Minbari enough to do all the stuff he did earlier on. But that's opening up the whole time-travel, circular reasoning can of spoo, and nobody likes to think about that stuff too much.
As Kosh would say, He has always been here (B5 and Minbar, not B4).
>!<
RADAR