How big does the hole in the backer board need to be around the shower valve? My current hole is big enough to remove the cartridge clip. What is the purpose of the large hole pictured in the directions? Larger hole=greater chance of leaking?
There is no official size for it. As long as the trim can cover it, it's good. I usually use the provided template. That works for most trims.
The benefit of the large hole is easy access to the valve in case you need to repair it. For example, my value has 2 screws allowing me to block the water from flowing to the chamber holding the cartridge. If I need to replace the cartridge, I don't need to shut off the water of the whole house.
There isn't a greater chance of leaking. As long as you have the proper seal/water proofing at the edge of the hole, you will be fine.