Naked mole rats and humans age for the same underlying reasons, the same types of accumulated damage. The difference in outcomes in terms of the shape of the mortality curve no doubt has to do with quality of repair mechanisms and resilience to particular forms of damage. Naked mole rats have less error-prone DNA replication, repair, and protein manufacture processes, a lack of lingering senescent cells pumping out inflammatory and destructive signals, a mitochondrial composition that is more resilient to oxidative stress (and they have plenty of oxidative damage, judging from the usual markers, they just seem to shrug it off; it doesn't cause further problems). The net result of this is that they do pretty well then fall off a cliff at the end.
It is interesting to speculate on what the cliff might be, a high threshold of damage needed to break an important repair mechanism, or a slowly accumulating form of damage that only really hurts the mole-rat at high levels, for example, but this is probably not very relevant to human medicine.
We know why humans age. We know what the damage is. We don't need to poke around in other species for further illumination in order to make progress towards rejuvenation - we won't learn anywhere near as much as we will from selective repair of the damage in humans or in mammals that are similar to humans. We don't need to improve human damage repair systems (comparatively hard) when we can repair damage (comparatively easy). It clearly takes a few decades for pathological levels of damage to arise, which gives plenty of time to deal with it through periodic applications of therapy, given a working repair biotechnology.
The comparative biology of aging is pure science, unlikely to produce meaningful applications of medicine when compared with other courses of action.