Is there a known reason why the filesystem in iOS is case-sensitive?
HFS+ originally ran on System 8 and System 9 and is case-insensitive. Apple developed the HFSX case sensitive file system around 2002-2003 as a replacement for UFS which was used by NextSTEP and could also be used by OS X.

In the transition from System 9 to OS X, Apple offered Carbon API's so that vendors could easily port their products without completely re-writing their applications. Carbon does not offer case sensitivity. For many years major vendors used Carbon code in their products, so HFS+ was left as the default file system.

iOS has transitioned to APFS but TimeMachine uses HFSX.