Why do LED retrofit instructions say to leave the ballast in the fixture?
First, that fixture looks permanently hardwired.  If so, you'll want to add a ballast disconnect. Code requires it, unless you argue that the fixture is now ballastless. But it's so darn convenient that I add them immediately upon starting work, and then, turn the power back on!

Cutting the wires off at the ballast is someting I only do to ballasts which are dead. It's already been wirenutted from the previous ballast swap, I would just do it at the wire nuts.  

Generally, ballast instructions are generic and simplified, try to come up with a universal instruction and you can see where it's hard.   Potential reasons for the "leave the ballast" instruction include:


different ballasts require disposal in different ways, and it's complicated and they don't want to open that can of worms
in particular, they don't want to scare the hell out of people with talk of PCBs
it may greatly reduce the weight of the fixture, with unknown consequences
it will shift the fixture's balance point, relevant to chain-hung fixtures
removing the ballast may leave holes on the fixture uncovered, which Code would disallow
in some bad installations, the screws holding the ballast also help hold the fixture to the ceiling.