What I haven't seen is a statement as to why this would have been a problem. The reason is that Q and Z were mapped inconsistently across various phone keypads. The present convention of PQRS on 7 and WXYZ on 9 wasn't settled on until fairly late in the game, and as noted, the airline reservation system, SABRE, is one of the oldest widely-used public-facing computer systems still in existence, dating to the 1950s.
https://en.wikipedia.org/wiki/Sabre_(computer_system)
The 7/9 standard, by the way comes from the international standard ITU E 1.161, also known as ANSI T1.703-1995/1999 and ISO/IEC 9995-8:1994).
http://www.dialabc.com/words/history.html
Other keypads may not assign Q or Z at all, or assign it to various other numbers, 1 for Australian Classic, 0 for UK Classic and Mobile 1.
http://www.dialabc.com/motion/keypads.html
Similarly, special characters can be entered via numerous mechanisms on phone keyboards.
My suspicion is that there's a contractual requirement somewhere to retain compatibility with an existing infrastructure somewhere.