Yes, I don't like the fact that those who work hard and honestly cannot afford the necessary work. Another dear friend in Texas may need rotator cuff surgery. She and her hard-working husband have discussed the matter; they cannot afford it. It seems immoral that though she needs surgery she cannot afford it.
But there is more to the morality of it than what you state: Our system, for all its faults, naturally favors those who choose to excel in their field. By contrast, those who choose to steal from their neighbors by taking an easy route, whether by doing mediocre work, or by not studying, or by not working at all, will find themselves left out.
DON'T HEAR WHAT I'M NOT SAYING. I'm not saying everyone who is poor is lazy! My Texan friend is a hard worker. Where they might have gone wrong is the choice of career path and education. But many do indeed choose the easy route. Earlier this year I was seeking to help a poor family move, get a job, get education. I could see them consistently choosing the easy route, and they suffer because of it. Their daughter suffered most because of it.
My dear Texan friend likely could pay for her rotator cuff surgery if she or her husband had a startup in which they poured their lives and passions into. (I am hoping to help them do just that.) The United States is in the top 10 countries for ease of starting a business.[1] (To be fair, New Zealand is single payer and is first. I'm not saying the system is perfect.)
Rewarding career excellence it seems to me has a broader impact on the culture around. Better workers pay more into insurance to help others. And better workers improve the systems and products that they touch.
Don't hear me say however that I think the system is perfect. I am a Christian and my command from Jesus is to help the needy, and we don't do that as well as I'd like. That's why I am aiming to bring better healthcare and careers to people in the poorest of nations. I have a side project I'm working on for the people of Haiti, and I don't see any reason it would fail to help many dozens or thousands (or millions?) of needy.[2] I have high hopes that in 20 years many more people in Haiti will be able to afford health care, and not because their government made it much more affordable or available. There is little hope of that in a corrupt nation like Haiti.
So I'm hoping to take the skills I have excelled in to help others to help themselves to improve their own skills, so that they too may be able to enjoy the same benefits I have.
TL;DR: There is more to morality than helping those who cannot pay. Our system seems to be, whether knowingly or unknowingly, guided by the "if a man will not work, he shall not eat" principle, and the moral response for those living under such a system is to both work hard to better one's own life and the lives of everyone who uses the products of one's skills; and to lend a hand to one's neighbor on an individual level, to help them to help themselves.
We all are guided by some form of absolute morality; please ensure yours takes into account all factors.
[1] http://www.doingbusiness.org/rankings
[2] https://news.ycombinator.com/item?id=16402404