I did write a letter. I bought a ticket for myself and my daughter to fly to SYD-IST-SYD, three months in advance. This would be my fifth return trip that year to visit my father with leukaemia. About two days before departure, his doctor called me to fly ASAP as these are perhaps his last hours/days. I called QFF to change our tickets to the first available flight, which was 24 hours earlier (22 hour one way trip as it was thru LHR), and explained my situation, very friendly operator offered to change our tickets, (are you sitting down?), for A$6250 each. When I said this were cattle class tickets already paid with wiles, not First or biz, and it's one way change, I was told that IS the cost to change a one-way FF seat in the last 24 hours. Finding this insane, but hoping to see dad, I changed the booking of my ticket, so my daughter could not make to see her grandpa alive. After I hang up Qantas I called my travel agent to re-check this with Qantas, he managed to cut this by 50%. On my return from funeral I wrote a letter to the big boy, I got a clear as mud answer, then when I called his office a staff member, whom I can't name here, told me "this is a profit maximising business, you need that seat and we have one if you pay, that's how capitalist system works", when I asked about understanding and compassion Qantas ads promote, he just laughed and hung up on me.
So, yes you can write a letter, your can be the best letter and has valid reasons/causes but this will take you to nowhere, they're there to make money.