This isn't about what's better for or how hard it is for parents, we're talking about what's more accessible to a child.
Again, you, your family, your neighbors may have been able to leap the learning curve and provide a fluent and immersive ASL environment for your child from birth. But most deaf children born to hearing parents are not brought into those ideal situations where they have immediate and full access to fluent ASL speakers at home and throughout their environment from the start. Parents and relatives may be slow in the first few years, with rudimentary and hesitant signing skills rather than the fluid and almost constant flow of spoken language and song children are exposed to. Most deaf children do not encounter the same amount of signing as spoken language on children's programming/DVDs. Most deaf children are not exposed to neighbors signing across the street to each other, in stores, to siblings and and their friends signing to one another at the same rate they see people speaking to one another.
A child with auditory access, whether through hearing aids or CIs, is -- in most cases -- going to be bombarded with more spoken language stimuli from the start than ASL stimuli. The shear volume of this input is going to have an impact. The child will be exposed to more spoken vocabulary, more frequently. That wash of continuous language exposure makes it easier for the child to learn the language.
This is one very important reason why we value my daughter's school for the deaf and are proponents of this option if available: they can provide an intensive ASL environment. Sure, we can easily provide access to spoken language ourselves: in her home environment, her local school, stores, restaurants, the gym, piano lessons, in TV/movies, etc., when we travel, she's awash with it. But we can't manufacture people using ASL everywhere we go. Her school provides exposure to other students, from her age group on up through high school, deaf or ASL-fluent teachers and aides, performers and other language models, a controlled environment awash with ASL flowing everywhere.
You may think it's easy for a child to access ASL in his or her own environment, that ASL is just free flowing around the average deaf child. But I don't agree -- I think ASL is far too rare in our everyday lives, far too difficult for my deaf child to encounter on her own, and I think we need to take pretty extreme action to make that's child's path to ASL somewhat easier. In our case, the school we choose, the deaf friends we make playdates with, deaf babysitters who know ASL, using ASL at home even when not directed at the child. This isn't necessarily making ASL easier for my child to access than spoken language, because the balance is still off, but it does make ASL more common in her everyday environment and that helps her learn the language.
we're all a bunch of slackers 
Just being around my son and other deaf individuals taught me a great deal. The only thing is, you have to be open to learning and seeing the obvious. Apparently, you are!
