Having a kidney transplant does not “cure” kidney disease. There are also risks, including the risks of surgery. After the transplant, you will need to take anti-rejection medicines, also called immunosuppressants, for as long as your new kidney is working, which can have side effects. You will have a higher risk for infections and certain types of cancer.
Although most transplants are successful and last for many years, how long they last can vary from one person to the next. Depending on your age, many people will need more than one kidney transplant during a lifetime.
https://www.kidney.org/kidney-topics/kidney-transplant
The majority of kidney patients with end-stage kidney disease do not simply die: they can survive several years on dialysis. As far as I can tell, most indeed do: only a minority of kidney patients ever get transplants.
Source: relative with kidney disease who would not accept a living donour kidney because of ethical concerns.
The US has a problem where there are a bunch of outfits whose income is derived specifically from dialysis, so for them transplants are bad business. Sure, the patient will (statistically) have a longer life and enjoy higher quality of life, but their income will be reduced so...
This results in a rather... muted endorsement of qualitatively better outcomes and where there's obviously also going to be an ethical component I'd say that's undesirable.
We all die. People with kidney disease die significantly sooner statistically if they do not receive a transplant, so this is the sense in which I mean saving a life.
"I decided to donate one of my kidneys to make someone's life a little bit easier for a little while".
And note that while dialysis is big business and I have no doubt that the people who are in it care far more about their profits than their patients, so are transplants. In fact transplants cost a lot more and make people a lot more money than dialysis and the only reason they're not as big business as dialysis is that there's just not enough donours, which makes a big honking red financial incentive to keep pushing for everyone to become a donour.
Meanwhile, like the National Kidney Foundation says, in my quote above, 'Having a kidney transplant does not “cure” kidney disease' and neither does dialysis. And because both treatments keep patients alive for longer than the typical five-year horizon of medical follow-up studies, they, both together, reduce the incentive to work on real "cures" of kidney disease (which, like cancer, is not one condition but many) which would make the sucking of dialysis and transplant both things of the past.
And I know this last one because I personally asked my relative's nephrologist and transplant surgeon about it and they were vague and hand-wavy, like "oh, sure, there's people working on that sort of thing somewhere".
But nobody's really trying because we can make millions keeping people tied up to machines or on immunosuppression until they give up the spirit and so who cares?