Why are prayers shortened when travelling but not when ill?
The sick are relieved too, often even more than travellers, only in a different way. Someone who is ill prays as their condition allows, standing, sitting, lying down, or in the end only in their mind.
The question rests on a mistaken assumption. The sick are not relieved less than travellers. In some respects they are relieved even more. Only it does not happen by making the Prayer shorter, but by letting its form adapt to their condition.
Someone who cannot stand prays sitting. Someone who cannot sit prays lying down. Someone who cannot move their limbs indicates the postures with a nod of the head. Someone who cannot even nod recites the words of the Prayer. And someone who can no longer do even that reflects in their heart on the meaning of the Prayer. One’s own strength determines how one prays.
Why is it arranged like this? A journey is easy to recognise. You set out, you are on the road, you come back. Illness, by contrast, has countless degrees. From a mild cold to severe paralysis there is no sharp line at which one could say that now the Prayer may be shortened. A single uniform rule would be too strict for one person and too lenient for another.
That is why the graded rule is exactly right. It takes every sick person seriously where they are, and never asks more of them than they can bear. It is the same principle that the first verse above states. God burdens no one beyond their capacity, whether on a journey or in a sickbed.