Food webs assume completeness. Are you assuming that any given reef tank will have a complete food web? While I can't prove it either way, my money is on every reef tank being an incomplete food web. For instance, the basis of most natural ocean food webs - phytoplankton and plankton in general are not largely present in our systems. How can you call that a food web?
How do you mean complete? Single phytoplankter species as producer and a single bacterial species as decomposer is a food web (chain in this case).
If it were a food web, you wouldn't have to put anything into it. (that is, feed)
You don't want anything in the tank to grow?
I know you and I generally see things differently, but I don't know how to explain it any other way. More biomass means you are supporting more respiration in your tank.
Sure. So have live rock and a sand bed and one fewer fish; problem solved. BOD also has a lot to do with the amount of decompostion going on. Our reef tanks don't have tons of decomposition happening at any one time. Now, set up a tank to mimic mangroves and dump in a bunch of leaves and bird droppings everyday and you'll see a pretty serious drop at night. But as Eric's articles recently in RK have shown, it doesn't particularly matter what is in the tank. There is always a decent BOD. Reverse lighted refugiums are probably a good idea no matter what is in the tank.
Let's say the power goes out, or an area of your sand becomes anoxic, there is a mass die-off of any given "niche-filler" or a food item is lacking for a certain niche-filler....you get the idea.
Well, power outages are bad for tanks. In a tank with fish but no rock or sand you're not going to have that much longer than a tank with all three. As for the sand becoming anoxic, 1. why is that happening in shallow sand, or 2. if it's only happening in deeper levels of sand that's normal, and why should I care?

Most sand and mud animals live in anoxic sediment. That's normal. It seems that most reef tanks have relatively higher O2 content in the sand (judging from a RK article from a bit ago), so why should that make us worry? As for species going extinct, there's no way to prevent that really. Reintroductions of new sand and/or rock every year or few years is probably a good idea. A lot of areas in nature tend to be patchy though, and there is probably overlap in the effective niche of most species. So while reef-like biodiversity is desirable, less than that is still quite functional.
Any way you look at it, more biomass is more potential nutrients and less under your control.
Why is this less under ones control? Most infauna are incredibly hardy anyway. Actions that will kill them in good numbers are probably wreaking havoc on everything else in the tank first (minus maybe treatments with things like flea-pills). I mean, should we all be worried when are corals grow larger that the larger biomass is going to be detrimental to the tank somehow? Lots of nutrients in that coral tissue and skeleton.
If I can achieve the same thing non-biologically, it is far more stable because it is completely under my control, not the fate of the organisms I am relying on.
Short of blasting down the tank and doing large water changes frequently, how are you going to ever maintain dissolved nutrients levels anywhere near natural levels? Without a lot of creatures actively consuming waste it will just be broken down by heterotrophic bacteria (no way to eliminate them but to sterilize the tank, which would kill anything we want to keep in it). Almost nothing is happening in our tanks that isn't directly mediated biologically.
Sure, there are some things (like nitrification) that are most easily and effectively done biologically - and with little associated risk. I'd never doubt that. But to say my tank is more stable because I have this or that population of worm or tunicate or whatever....and I rely on it is just not within my logic.
Ok. Nothing says this must be done, but it is an aweful lot easier to let organisms do the work naturally than to try to deal with every little transformation that needs to happen. Our technology just simply can't provide most of the functions that reefs and adjacent habitats provide.
Now in nature, I'd never argue this point. In a reef tank...an incomplete ecosystem, it's a different story. I like to look at little critters as much as anyone. But I don''t rely on them and I certainly don't expect them to take care of my tank.
Ok. Again, what are you considering "incomplete?" Biodiversity improves the efficiency of resource usage, but so far as is known (really, really hard to do these studies) it probably doesn't take a lot in most cases. Often the apparent "extra" biodiversity provides system stability through overlap in the effective niches of species.
As for not relying on creatures to perform certain transformations in your tank, that's fine with me. The easiest-to-run, most succesful tanks I've ever seen tend to do this, and these were also the most naturalistic in appearance and behavior (and the most visually appealing to my eyes) as compared to a reef. I don't see that avoiding live rock makes keeping a tank any easier or that any of the animals in it are likely to perform better. If anything it seems just the opposite so personally I don't see any reason to try it. It probably can be done, but I've also seen great tanks with deep beds of crushed coral, or Acropora doing very well under NO fluorescent bulbs. Sure, these things can be done, but they don't seem like the easiest route, so I really don't see the point in entertaining them to be honest.
Best,
Chris