One wouldn't say that all chronic illnesses affect a person's physical capacity; but many of them do. A person with an incurable lung disease or a person with a heart defect, for instance, are in much the same boat that we are, in the sense that their aerobic capacity is permanently limited. In our case, the limitation is occurring on a cellular level; it's more obvious and easy to see in someone who can't breathe well enough to get sufficient oxygen to their muscles, or whose heart does not have the ability to circulate their blood at a normal capacity.
Another way to look at certain types of chronic illness is that the ill are being perpetually re-injured every moment. A Paralympic athlete who at one point lost limb(s) had a long, long recovery process before they could even be fitted for a prosthetic, and still longer to train as an athlete. But our injury process is unending, and is made more severe by more physical effort. A person can't heal from a broken bone if they're required to get up and dance on it all day. Now imagine a person with an incurable brittle bone disease who has broken their leg, and they have to get up and dance on it every day. Not only will the original injury not heal, it will become worse, and other injuries are very likely to occur.
The analogy with ME/CFS is that for us, "dancing" is the simple act of using energy in order to live and move. And as we all know, we cannot train ourselves out of that situation.