There's a few reasons. Firstly, from a production standpoint, we just didn't want to deal with it, what with the first episode taking at least a year longer than we had originally planned. I do regret a bit that we didn't do a defend-the-base mission like we originally planned - but you have to bear in mind, that mission would still have been the end of the line for Bradshaw. He would not have returned to Confed afterwards.
And that's the second thing - even had Bradshaw been given an amnesty, he would not be in command of the Firekka's wing. That would have been out of the question, if only for morale reasons (it's really not too encouraging for those who stuck with Confed, didn't go around shooting at their wingmen... and end up getting passed over for a command position in favour of a traitor). So, that would have had a very dramatic effect on the rest of the game, and we couldn't accept that.
A third consideration is that Bradshaw simply wouldn't have gotten out of this alive. Sparrow and the rest of the Guadalcanal pilots could get out of prison - but he wouldn't have. It's one thing when you're dealing with a small mutiny that you know a lot of your officers sympathise with to some degree - but it's another thing entirely once those mutineers start encouraging others to take up arms. Then you have to set an example - so Bradshaw would have had to die in order to get a point across to the rest of the Confed fleet. The same thing would naturally happen to the Guadalcanal pilots, though according to the losing ending, they escaped leaving Bradshaw behind, so I guess they might have survived as pirates.
Of course, all this assumes Bradshaw's capture - but had he not been captured (which was indeed supposed to be a possibility - that mission we cut out wasn't meant to be an unwinnable fight-until-you-die scenario), he still wouldn't have returned to Confed. Not only would he not have had time to even contact Confed before the battle (things happened pretty quickly, once the Kilrathi blew up the chiefs of staff), but even if he had, I'm not too sure if they would have granted him amnesty. Again, there's a difference between amnesty to a bunch of captured, contrite mutineers, and amnesty to a bunch of pirates (because what do you think Bradshaw would have done, had he gotten away? Started up a jazz band?
). And finally, even if he had been granted amnesty, we come back to the fact that there's no way he would have been put in charge of the Firekka's wing.