Your father and Sirius here were the cleverest students in the school, and lucky they were, because the Animagus transformation can go horribly wrong — one reason the Ministry keeps a close watch on those attempting to do it.
From that it sounds like it may be like learning to drive in the real world. You have to apply for a license/permit so that you can actually begin the process of learning (under the supervision of somebody who is already qualified), then later on pass a test to prove that you're capable of doing it safely.
In that case it likely wouldn't be an option to just turn up one day claiming that you've suddenly learnt to be an Animagus. It's a particularly difficult bit of magic, not something anybody (except perhaps Dumbledore) is going to master overnight. To do so would have raised a lot of suspicion and resulted in some uncomfortable questions from the Ministry.
Lupin also shares his personal reasoning for not telling Dumbledore about the others' abilities at the end of Prisoner of Azkaban:
Lupin’s face had hardened, and there was self-disgust in his voice.
“All this year, I have been battling with myself, wondering whether I should tell Dumbledore that Sirius was an Animagus. But I didn’t do it. Why? Because I was too cowardly. It would have meant admitting that I’d betrayed his trust while I was at school, admitting that I’d led others along with me… and Dumbledore’s trust has meant everything to me. He let me into Hogwarts as a boy, and he gave me a job when I have been shunned all my adult life, unable to find paid work because of what I am. ..."
Even if the other three Marauders had "gone legit" I think Dumbledore would have seen through it, even if nobody else had, knowing those four as well as he did. Lupin may still have had reservations about implicitly admitting that he'd betrayed that trust.
And one final consideration: It appears they went almost straight from Hogwarts to joining the Order of the Phoenix, so becoming registered Animagi likely wasn't a major concern for them at any point prior to James' death.