No, I get it. It's not just the neighbors you're worried about. It's squirrels, cats, dogs, fruit flies, flies, raccoons, ground squirrels, birds, opossums, rabbits, etc.
I truly think it depends on the person and their perception of what is "proper" or acceptable.
I personally don't care if they do get in the compost pile. It doesn't bother me at all. But that's just me. Nature has a way of taking care of it's living animals. I don't feed them intentionally but if they find something I have discarded to be useful as sustenance, I'm ok with it.
Our neighborhood has opossums that scout the territory diligently. I know because when I go out at random times throughout the evening to the garden to harvest fresh herbs or vegetables for dinner and turn on the light, I see them at least once a week. I've lived in the same place for five years and never seen one in my compost pile. Perhaps I should be insulted. ;)
Insects are an essential part of the system of breaking down the materials that comprise the compost pile. I'm ok with them too. Some people have a problem with ants, that's simply a sign they need to water their compost pile. Some people have a problem with slugs which is a sign they need to turn their pile and let it dry out a bit. I haven't had a problem with either but I usually maintain an even distribution of browns , greens (carbons, nitrogens) and water and oxygen.
I understand where you're coming from but the animals just don't bother me. Again, it's all relative to each human's perception.
I haven't yet described anything that would indicate that I am doing anything that promotes "the most efficient breakdown of the waste". Throwing eggshells on top whole and throwing whole leaves brown (pin oak at that!) on top is far from efficient. If I was efficient I'd crush the eggshells in my hand, sprinkle them evenly on top, then sprinkle fresh grass clippings, sprinkle an even layer of shredded leaves, fluff the top layer and then water the top. But I don't have time to do that every time I add something to the compost pile.
If you really want to discuss efficiency, here is how I started my compost pile and I have reconstructed my pile the same way twice already this year. (I like doing it if it's not hot outside.) Here's what I did when I learned about composting and really focused on on it the first time years ago.
I did my research, it was Spring.
I had 11 large garbage bags full of pin oak leaves from the fall before. They're huge but they had broken down a bit thru winter.) Anything not broken down was run thru a leaf mulcher.
I had fresh grass clippings from a neighbor. (Now I get them from asking random people mowing their lawns and from the yard waste recycling center as people are getting the bags out of their car to haul them to the dumpster.)
I had some leaf mold from under a huge pile of leaves.
I had gumballs from the gumball tree from a neighbor from the previous fall.
I had maybe five gallons of compost from another source.
I lightly layered everything by literally loosening everything and sprinkling it in my 5x5 wire bin. Sprinkled grass evenly along the bottom, sprinkled leaves evenly on top, repeated a few times, sprinkled compost to distribute beneficial organisms, repeated grass, repeated leaves, sprinkled leaf mold, repeated grass, repeated leaves, sprinkled gumballs throughout the center and kitchen scraps as well, repeated grass, repeated leaves, etc until I was out of material. My pile reached a good four and a half feet high. Was light and fluffy because nothing was compacted so plenty of oxygen available throughout. Watered over the top with a hose. It only took a couple of hours to do everything.
Within a couple of days I could see the top of the pile was visibly getting lower based off the horizontal wires of the fencing I was using. So I went outside to stick my hand in the center. It was much warmer than I ever imagined since this was my first experience - it was in fact - hot to the touch.
A couple of more days and it continued to lower. I stuck a digital themometer probe from the kitchen into the center of the compost pile and it read 165F. Success! Although had I known about beneficial organisms being killed off 155F - 160F and higher, I would have moved the center portions out and turned the edges in a bit. Anyway, I have usable compost well within four weeks!
The key is balance and even distribution of all materials whenever possible greens, browns, water, oxygen, etc.
And if you really want to "jump start", you can find other nitrogen sources like urea, alfalfa pellets, fresh manure, etc. But if you have enough fresh grass clippings and you mix it in thoroughly it should to fine.