Narcissists are broken people incapable of self-reflection and everything centers around them.
They see everything in the world as being put here for their enjoyment. They thrive off of attention (negative or positive) and it's the only time they feel alive.
The OP could very well be a person just realizing that they want to focus more on others and this is a completely normal stage of life that different experiences or perspectives can help with.
Nearly everyone is capable of self reflection. To think that an individual is categorically incapable of it is to deny them their humanity.
it has dumbfounded me at times because I, as you, thought everyone has some sense of it and if they saw it they might change; but alas not always the case
There is difference between having the ability to self-reflect, and having a proclivity to self-reflect. Neither is the same as doing so effectively, and neither speaks to the question of having a motive to make further personal changes as a result.
The comment to which I was responding categorically denied certain people from having even the ability. Ever.
I would add that Narcissistic Personality Disorder, like all personality disorders, is essentially unfixable [0]. However it's unlikely that OP has NPD, since someone who actually has an NPD would not be aware if it.
[0] According to my psych friend.
I was able to self-reflect very well, and criticize myself to obliteration. The thing is, normally, I already feel like I do as well (regardless of whether I do, regardless of how other see that). It hurts too much. In the two examples I mentioned, no such pain was felt. None whatsoever.
Obviously, I don't recommend one getting a psychosis, but there are benefits to it (FWIW, I had multiple, mostly short ones, and one long one).
([1] For the record, I'm indifferent and unsure about your case.)
Aside from that the term narcissism just means self-loving. It comes from the Greek after a person named Narcissus who fell in love with the sight of his own reflection. People can experience and express variant degrees of a selfish nature without being mentally broken. To call somebody a narcissist literally means the targeted person is primarily selfish.