Full feature support would be the main benefit. The core kernel/OS would receive frequent updates.
Where those features/updates benefit a CShell enabled UI/feature/function then the benefit would be felt on mobile at the same time as the Desktop/Tablet/Xbox/IoT equivalent.
There seems to be a complete misunderstanding of the convergence of OneCore and the purpose of 'Windows on Arm' and Adaptable CShell.
Cshell is what you see - the UI/UX User Interface/Experience. Cshell is an interpretive layer that sits on top of the core/kernel exactly the same as the existing Shell, but the fuss is all about how this new adaptable shell is context-aware and will shift to fit the display/interface at any given moment.
As a 'traditional' mobile it would look and function exactly as Windows 10 Mobile currently does - plug in a screen and *magic* it's Windows 10 Desktop (assuming WoA and Cshell ever arrive in full).
Windows on ARM is pivotal in the above being possible on a mobile device (without a x86/x64 processor).
Windows on ARM introduces multiple emulation, kernel and driver-level interfaces, or in laymans terms allows these various parts of the windows system, it's hardware and software to communicate. Intel and AMD based x86/x64 processors communicate in a completely different language to the ARM-based processors common in tablets, IoT devices and smartphones.
Neither Windows on ARM or CShell are a magic bullet on their own - the combination of these development (if ever released to phone) would ensure the future development of the platform and extend its' feature-set.
The sad, insulting, truth to all this is that Microsoft have tested WoA - it works (*on existing sod*ing 820 chipsets, cough 950, cough Elite X3*), they have already accidentally released a mobile build that includes CShell, but they refuse to say diddly-squat about mobile, give any indication of commitment and leave us all to wish, pray, attack each other and the Windows Mobile Insider and Mobile communities implode.