if you have haxchi, not cbhc, you "can" keep it. it's not a problem to do so.
Just remember to NOT run both at the same time. for example, if you set Tiramisu as autoboot, then don't run haxchi to access HBL or it'll try to re-patch the kernel. just run Miimaker instead.
You could still use Haxchi shortcut for example, instead of Haxchi Kernel patcher. If you changed haxchi config to automatically patch the kernel when not pressing a button, you might want to edit the config file to prevent patching it accidentally (or even completely remove the kernel patching from the config file, but keep it, you never know when you'll need it) and keep only the shortcuts
Personally, I'll keep both.
Like Maschell said, the guide tell the users to delete it only to be cleaner. and you can play the NDS game again if you like.
But if you know and understand what you are doing, you can keep it.
@Maschell :
Can we use Haxchi to launch HBL and run the payloadInstaller ? I suppose not as github says "it needs to be installed from the injection itself".
It would be more stable to launch HBL from haxchi first than trying to launch the web exploit, freeze and reboot and clear cache.
Can't it be a homebrew elf? Or does it requires to be a web exploit to launch payload.elf ?