Imagine a person who has no access to hot water. Now this person has to endure cold to pray, and the other person can easily pray with hot water. How is it fair for cold water person to endure such a pain?
Extend this example to people with back pain injuries, how is it fair for this people to endure such a pain while others are easily doing their prayers.
Most of people don't have a complete understanding of ALLAH and his way of guiding the world and his creature. as I always advice people: go study Aqidah and the meaning of ALLAH's names and adjectives.
The first thing is to believe that ALLAH is not to be questioned and we are, this is his property, and he does what he wants, this is the key to the answer.
In the hadith:
عن علي رضي الله عنه قال: كنا في جنازة في بقيع الغرقد فأتانا رسول الله صلى الله عليه وسلم فقعد، وقعدنا حوله ومعه مخصرة فنكس وجعل ينكت بمخصرته، ثم قال: ما منكم من أحد إلا وقد كتب مقعده من النار ومقعده من الجنة” فقالوا: يا رسول الله أفلا نتكل علي كتابنا؟ فقال: "اعملوا فكل ميسر لما خلق له" وذكر تمام الحديث. ((متفق عليه)
**We were accompanying a funeral procession in Baqi` Al-Gharqad (graveyard in Al-Madinah) when the Messenger of Allah (ﷺ) proceeded towards us and sat down. We sat around him. He had a small stick in his hand. He was bending down his head and scraping the ground with the stick. He said, "There is none among you but has a place assigned for him either in the Jannah or in the Hell." The Companions said: "O Messenger of Allah, should we not depend upon what has been written for us (and give up doing good deeds)?'' The Messenger of Allah (ﷺ) said, "Carry on doing good deeds. Every one will find it easy to do such deeds (as will lead him to his destined place) for which he has been created." **
So, your understanding of WHY anything is the way it is, will not change the fact that You are oppressed and God is compelling and almighty.
A person enduring cold water is rewarded more for enduring this, and an sick person can pray in many ways as in the hadith:
حَدَّثَنَا عَبْدَانُ، عَنْ عَبْدِ اللَّهِ، عَنْ إِبْرَاهِيمَ بْنِ طَهْمَانَ، قَالَ حَدَّثَنِي الْحُسَيْنُ الْمُكْتِبُ، عَنِ ابْنِ بُرَيْدَةَ، عَنْ عِمْرَانَ بْنِ حُصَيْنٍ ـ رضى الله عنه ـ قَالَ كَانَتْ بِي بَوَاسِيرُ فَسَأَلْتُ النَّبِيَّ صلى الله عليه وسلم عَنِ الصَّلاَةِ فَقَالَ " صَلِّ قَائِمًا، فَإِنْ لَمْ تَسْتَطِعْ فَقَاعِدًا، فَإِنْ لَمْ تَسْتَطِعْ فَعَلَى جَنْبٍ ".
Narrated `Imran bin Husain: had piles, so I asked the Prophet (ﷺ) about the prayer. He said, "Pray while standing and if you can't, pray while sitting and if you cannot do even that, then pray Lying on your side."
So a person who was injured and have hard time praying is fair with respect to ALLAH's will, but not fair in the human meaning of fairness and justice, and we can't compare ALLAH's fairness with our fairness, this our limit and we can't go beyond it, and the utter faith is to truly believe in this and don't try to spend time understanding the divine way of handling life, and get busy do what ALLAH command us to do. It was okay to ask, but not okay to keep going this way.
