Naturally, these stages would overlap, and the exact species involved may vary greatly, but the above is a general representation of what happens on a coral reef as nutrient levels climb.
So..... If we start a reef tank with clean rock, clean sand, and clean water, we create an environment that closely resembles the reef at the beginning of the scenario above. Where it goes from there is in our hands. If we keep the system relatively clean, and low in nutrients, we can support a reef that closely mimics the reef at the beginning of the scenario above. The higher we allow the overall nutrient level to become, the more rotting organic matter we allow to accumulate, the more tiny poo eating infauna we support, the closer we push the system to the conditions of the reef at the end of the scenario above.
This is a bit of an oversimplification. While eutrophication has certainly caused problems for many reefs, a lot of experts attribute the damage seen on a global scale just as much (if not more) to climate change and overfishing.
It's also not accurate to describe a pristine reef as being free of algae, detritovores, or filter feeders.
I recently spent some time on Ningaloo Reef in WA, and it is about as pristine as pristine gets. Extremely few humans around, no farms, and strict environmental protection to the point where most boat traffic is prohibited and not even a single shell can be collected without cutting red tape. The nearest large human presence is hundreds of miles away.
There was plenty of algae growing, there were just also plenty of algae eating animals. Schools of parrots, angels, and tangs numbering well into the dozens would swim about scouring the reef and cleaning it of algae. There were green sea turtles that fed on larger growths of macroalgae and sea grasses. Filter feeders were abundant, because there was so much food in the water (in the form of plankton, marine snow, and bacteria) that it could actually be seen as a fine haze limiting visibility to under 50m in many places.
The sand (bordering right on giant growths of acroporids) was teaming with pods, worms, and god knows what else. Corals we think of as liking "dirty water" like some of the hardiest LPS and filter feeders were growing right next to, and often under corals we think of as liking "clean" water (acriporids).
Coral reefs are not nutrient poor environments. They are so unique, diverse, and densely packed with life because of how efficiently the scavenge and how tightly they recycle nutrients in the ocean. One could compare them to lush oases in an otherwise barren desert. In terms of primary productivity, the only ecosystem in the same league is the tropical rainforest. IIRC, coral reefs win in terms of biomass per cubic meter.
A reef is full of micro-niches, with many animals we think of as having fundamentally different care requirements living within feet to inches.
I saw many places where a giant growth of an SPS coral like hydnophora would have LPS corals like fungia, acans, or faviids living on the sand (yes, the sand) right under it, slightly shaded. On its very bottom, almost completely shaded, obligate filter feeders would grow. In the sand around it, there would be tridacnids, goby/shrimp burrows, wandering sand sifters, and PLENTY of creepy-crawlies ready to eat any organic matter that settles to the bottom un-noticed.
It was fascinating to see. I've never been to a fringing reef before, nor a reef that was so incredibly healthy, and it really made me rethink or abandon a lot of the paradigms of our hobby. It also made me start feeding my corals much more heavily.
I personally run a BB, but not because I'm scared that a DSB will crash my tank. I run a BB so that I can run more flow without needing to worry about sand storms.
I just think the notion that a sandbed with lots of critters to recycle nutrients, or a tank with constantly growing biomass is not somehow antithetical to what one sees on a natural reef. I'd wager that virtually all tanks hobbyists keep are lower nutrient (in terms of biomass or available coral food) per cubic meter than pretty much any wild reed. The challenge for the hobbyist is keeping those nutrients in the right form (not pests), which can be a bit more challenging to accomplish in captivity.