Doom's rejection of Namor's plea for help simply because Namor didn't ask him first, and that offends Doom's pride. Fans who also read AXIS know that Magneto didn't make the same mistake a few months earlier (in comic time).
Despite being a collection of intelligent men, the Illuminati don't seem to have any real ideas beyond "blow it all up!" However, given an early issue of Hickman's Avengers shows the Superflow being destroyed, this makes sense. The Superflow is stated in Newuniversal to be where ideas come from, so no wonder everyone's being so single-minded.
If Captain America managed to capture the Illuminati with SHIELD, it would have been pointless (even if incursions somehow ceased to be a problem at some point along the way). He can't send them to prison, or make them stand trial for destroying a world. Even is morally wrong, judges make sentence based on laws, and which law talks about this? The people from that alternate dimension are all nonpersons for the legal system, their existence has never been recorded and legally recognized. Even more, who is to say that the Illuminati destroyed a world to begin with? Is there any witness, besides the Illuminati themselves? No, judges would laugh to Rogers if he sends those prisoners and asks to start a case. In fact, he may get in problems himself, for sending a US military force in such a pointless wild goose chase.
