Bradwell wants the truth, the whole truth, and nothing but the truth. And he's not afraid to admit it:
I'm not like El Capitan. He wants to bring the Dome down. And Partridge, he wants to get back at his father. I just want everyone to know the truth. (8.11)
The problem with Bradwell is that his search for the truth is:
Bradwell is stubborn, and sometimes we just want to reach into the book, give him a quick slap on the wrist and say, "Cool your jets, Bradwell."But, like El Capitan, Bradwell's another one of our heroes. He didn't need to follow Pressia, and he countlessly puts his life on the line to save his pals.
And above all, he surprisingly doesn't hold grudges. When El Capitan kisses Pressia, we expect some kind of physical or verbal thrashing. Instead, we get:
I couldn't leave you here to die […] because you're like a brother to me. Both of you. (68.53)
Now that's the true definition of being a bro. And that's what Bradwell is: an ambitious, strong, single-minded bro. Sure, he's got quite the temper, and his search for the truth can be frustrating, but without Bradwell there's simply no way that Pressia and El Capitan would survive.