The original commands quoted are:
أَقِيمُوا الصَّلَاةَ — establish prayer.
كُتِبَ عَلَيْكُمُ الصِّيَامُ — fasting has been prescribed for you.
The majority reasoning just studied would keep the equivalent duty outstanding. Alongside that reasoning, a separate Quranic text also addresses fasting after illness or travel:
فَمَنْ كَانَ مِنْكُمْ مَرِيضًا أَوْ عَلَى سَفَرٍ فَعِدَّةٌ مِنْ أَيَّامٍ أُخَرَ
Meaning: whoever among you is ill or on a journey is to fast an equal number of other days.
Notice the same number of fasting days, not an unrelated self-chosen substitute. The reasoning that a new text is not necessary does not mean that no separate text exists.
- Original Commands and the Fasting Text