Why doesn't Wolverine body expel adamantium skeleton?

I understand it's a fictional character and his properties are such as his creators want them to be.

That said, is there a logical, plausible explanation that I miss? The one that would be consistent within the constraints of the X-Men Universe.

I mean, I remember seeing said superhero expel a bullet from his head. It did not get stuck there, the body removed a foreign object. So that should be the property of his regeneration, removal of foreign objects stuck in the body.

Assuming his ability to regenerate is infinite and doesn't have to obey any energy conservation law, why didn't his body expel the metallic skeleton, and then rebuilt a proper skeleton? It should the skeleton to be a bullet, only larger.

Why did it accept is as a replacement for bones?