The only real fact is, if Chief didnt go in when he did, He would of not had the upper hand when the Didact STARTED to nuke the planet. Do you think any UNSC ship was going to stop him, even a fleet? I doubt it.
If things went Del Rio's way they would of all been dead, Master Chief too, he would of never ran into the Librarian. The Chief is more than a investment and machine. Hes a human and that was the point of the game. He has intuition to do things that need to get done right THEN not later, he was never programmed for later, Captain Keys saw this, when things went nasty he said "Chief we need your help" just like Lasky. It was never a command, it was a request because the Chief has a better judgement on the battlefield, he was designed to be a one man army, captain to the grunts.
Del Rio tried to talk down to the chief like he was a fool, when he knew he was the reason that the humans won the covenant war. He was assumed MIA for 5 years, and then turns up...do you think you should argue with this guy who had figured out a way to stay alive. Should he have worried about his ship? not at all, its not about the money at this point, its about the race of humanity. Its bigger than the few thousand lives that maintain the ship. Chief knew what had to be done, brought information to a figure head not asking for permission to go, but instead reinforcements and warning of the impending doom.
Del rio should return and get flood infected and become some evil dude