Actually, end stage renal disease (ESRD) including both dialysis and transplants, is covered by Medicare regardless of age. The only other condition that enjoys this status is amyotrophic lateral schlerosis (ALS). I have no idea why ALS is handled this way, especially since there are several similar motor neurone diseases that aren't covered, but in the case of ESRD, it's because when dialysis was first developed it was extremely expensive and insurance refused to cover it. The result was few dialysis machines were built and the costs remained very high. ESRD was and is very common, so laws were passed to extend medicare to cover it. (And the costs did drop, but it's still expensive.) And when transplants became available, the coverage was extended again to cover that.
There is, however, a little gotcha in all this. The drugs needed to prevent rejection of a transplant are also expensive. And once you have a transplant, you don't have ESRD any more, so your Medicare coverage ends. This was addressed by extending the coverage for 18 months, which I guess is how long transplants used to last. But these days the average is more like 9 years. So what happens is someone gets a transplant that's paid for by Medicare, their meds are paid for for 18 months, then the coverage stops, they can't afford the meds and the transplant stops working. So they go back into ESRD and need dialysis, at which point they're covered again.
This is absolutely insane no matter how you look at it, since the meds are typically around $10K/year whereas dialysis is closer to $50K/year. So not only do you waste a precious organ, it ends up costing more.
The good news is that one of the provision of the AHA that goes into effect in 2014 is to extend medicare to cover the meds indefinitely.