I am not 100% sure but my educated guess is: it is because the ArcGIS Server core is based on TomCat web server which is case-sensitive in its nature. I believe it was possible to change the case-sensitivity of all urls in TomCat of earlier versions but am pretty sure it is hard to do in the current version used behind the scene in ArcGIS Server 10.1+.
Using a Web Adaptor with a web server where you could have case-insensitive links does not solve the problem (or better to say does not alter this behaviour) since the URLs will be anyway redirected to TomCat used in ArcGIS Server. So, you just have to use case-sensitive notation for your URLs.
If you have some time and want to play with the settings, go ahead to
C:\Program Files\ArcGIS\Server\framework\runtime\tomcat. TomCat documentation is here. However, keep in mind that editing the underlying TomCat settings is discouraged and may result in corrupted installation of ArcGIS Server. Esri does not support these workflows so you will not get any support on this. And please never do any of this in production, set up a sandbox machine for testing.