I never realized that Luke Cage had a "healing factor," but there it is in the Marvel Super Heroes r.p.g. rules, 

Powers

Body Resistance: Resist both physical and Energy attacks with Incredible ability.

Regeneration: He can accelerate his healing rate at Typical levels.

Only Typical (6 hp/round), as opposed to Wolverine's Monstrous (75hp/round), but still, there it is.  The show made this big deal out of it, calling it "the key to immortality."  That got me to thinking about this 2015 review paper by Crespi & Go, which shows that the situation is more complicated than that.  In cellular terms, immortality is not a good thing.  The most famous immortal cell line, HeLa cells -- made famous by Rebecca Skloot's The Immortal Life of Henrietta Lacks -- was derived from an ovarian tumor.  That's right.  To a biologist, immortal means cancer.

Figure 1 of the paper lays out the logic of trade-offs, which are a major concern of evolutionary biology.  Having really big muscles also means you burn a lot of energy (and thus starve faster).  There's no way around that conflict, which is why it's called a trade-off.  Some diseases go together, like diabetes and heart disease.  Others oppose one another; raising the risk of one lowers the risk of the other.  The paper goes on to describe several pairs of diametrically opposed diseases.  For this post, we only care about Part 3: cancer vs neurodegenerative diseases.

Having really effective DNA repair mechanisms, as a regenerating person would, means two things.  Yes, that person is less likely to have cells die spontaneously, due to aging or a degenerative disease, or due to various super-villainous toxins or radiation-based energy weapons.  However, and here's the kicker --

His tumors would be equally hard to kill.

And with bulletproof skin, surgery would not be a good option.

Why would a regenerating person ever get cancer in the first place?  Well, because every time a cell divides, it has to copy its DNA.  Every copy is an opportunity for a mistake.  This is why most cells, especially neurons, stop dividing once you're an adult.  It's a cancer-minimizing strategy.

Wolverine supposedly gets around this by having an extra-aggressive immune system.  Unfortunately, the way immune cells generally kill cancer cells is through triggering the apoptosis mechanism mentioned in the paper.  I have a feeling that regenerating cells would not be easily triggered.

So Immortality?  I don't think so.

Of course, all this is fictional, but it's fun to think about.  Being a science geek has its perks.

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