Me either, tbh I’m not sure I’m comfortable with Swanwick being Martian Manhunter at this stage given he didn’t get involved with the Kryptonian attack or the Doomsday one. It raises too many questions imo.
I think I can see some reasons he'd stay out of those fights.
First off, we don't know exactly when he came to Earth, could be he didn't take on the Swanwick persona until after MOS, or even after BVS. Maybe there is a real Swanwick who he only impersonates sometimes.
Putting that aside, lets assume he's spent years on Earth as Swanwick, not coming forward because of the same kind of fears Clark had in MOS. When he sees the reaction to Superman: giving him up to Zod, the army initially treating him as an enemy in Smallville, all Manhunters fears would be reinforced.
Manhunter might be conflicted over the kryptonian/human struggle. Zod is one of the last survivors of his race, he saw his planet die, which J'onn would sympathise with. If given a chance to bring Mars back to life at the cost of the Earth, he might have difficulty deciding.
If you aren't a human, the situation doesn't seem as clear cut, J'onn could struggle with the weight of deciding which species should live, and which should die.
I could go along with the idea that given these thoughts, he decided not to use his powers, to act only as the human he is portraying and let nature take it course one way or the other.
In BVS it's a bit cleaner, we hear him say himself that every attack on Doomsday makes it stronger. He has no reason to think his personal attacks will succeed where missiles failed, he'd just be making Doomsday more powerful.
Plus there was fire all over the battlefield, he'd be half dead before he got close to the fight.
