The only real "expert" on carp on this forum is Fishbreeder and when he talks y'all don't listen or you attempt to scrutinize his post. So why ask for an expert opinion if you don't plan on listening? The man has been a fish biologist longer than I've been alive.
I'm appreciative of the few folks who do seem to gather a tad bit of edumification from the few things I do know about an' I do try and restrict my commentary to those few subjects...for the most part.
Now I done spent a lot of time with some gin-u-wine experts an' ain't so sure I put myse'f in that group, but that's neither here no there.
Gen'rly speaking the original post's supposition is correct. However, in practice its a tad more complicated so I'll provide a fer instance....
Most of the time the carp population is being "managed" if you will, as a negative influence on the primary species of concern, usually largemouth bass. For a very long time you can have a very good bass fishery alongside a carp fishery and you may never even know the carp are there. A lake with a solid bass population with good habitat and water quality may also have a population of a few, sometimes very large, common carp. While the carp population does remain stable, it never expands to the point of dominating the water body as long as conditions remains favorable for the bass in the lake. The bass do indeed, along with the sunfish and other species of the typical bass lake, eat almost all of the carp's reproductive efforts. Only enough survival and recruitment to maintain a few, really big carp. The carp getting so large due to lack of competition for resources (all you can eat) and good water quality (clear and clean).
Then the lake manager does something drastic to change things. Say kill ALL the grass with a large dose of herbicide in the early spring. Maybe put in too many grass carp along with the treatment. Just hates all them dang weeds. So, all the grass gets gone and it comes a big storm and the wind stirs the lake and a lot of muddy water comes in too. In the past it'd settle out in a day or two. But now the weeds is all gone and it just don't settle down good and quick. Meanwhile them few carps has a good spawn in the new water and a big hatch.
In the past all them fry got ate up, but its too dang muddy now for them to be easily seen, and the weeds what died after the treatment made the water rich with plankton for them baby carps to grow fat on. Which they do remarkably fast and before you know it they are nine inches long and most of the bass (that can't see 'em ennyhow) can no longer catch and eat them. So a lot of them gets to a pond and a half, and then to three pounds.
Now we got a lake full of three pound carp that stays stirred up all the time and the bass done all starved to death except a few that learn to live in muddy water. Meanwhile they's so many small carp they done ate everything organic in the entire lake and are sifting the mud all day for scraps. They spawn once more and the mudhole is full of thousands and thousands of small carps that can't grow 'cause they's so crowded and they ain't no food.
So it may not be the number of predators it may just be the availability of the carp offspring to them. In the event of an ecological disturbance, manmade or natural, common carp are among the very best of opportunists and will take full advantage.
I've seen the above scenario many times. But that don' make me an expert.....