You're forgetting that the planet they were living on was so hostile to life, most chidren never reached maturity, and the adults died left and right. Only the strongest, and luckiest, actually survived. They needed the high birth rate in order to combat this and keep the species going. Out the thousands born, only a few would actually survive until adulthood, and considering there are animals who leave their young to themselves, it is possible that this is what Krogan did before they went off world. Once they had a means to keep all their children alive until adulthood, their population exploded. In a few hundred years they were swarming the galaxy.
It would be like i crocodiles somehow learned how to make sure all their eggs hatched and grew to maturity. Crocs lay up to 100 eggs at a time, but most die before reaching maturity. If they didn't, then the crocodile population would explode, prey would become scarce, and they would spread to find new prey. Literally no different.
No, this is the genophage. Krogan at the time of Mass Effect have not been able to have many children for a long time because of it. Most of their children are stillborn. So yeah, NOW they don't have a huge number of kids, but that's the whole point of the genophage. It contradicts nothing. it is literally the story.
It's also very difficult to infer any information by looking at a single slide.
The rest of your post is confusing, because we don't know how long it takes for a Krogan to reach maturity, but we do know they were able to be grown quickly to be soldiers for a war. That, itself, would suggest that they have an abnormally large breeding rate. And that suggests a fairly quick maturity rate. So you give evidence for them having high birth rate and quick maturity rate, but seem to be claiming that evidence shows the opposite. And I'm not sure what you're talking about them being child prodigies. They're an intelligent race that matures to adulthood much, much faster than humans do. By our standards yeah, they would be 'child prodigies'. They're easily as intelligent as any other race, they have engineers and scientists. And they piggyback off of other races.
I'm not saying there aren't inaccuracies in the game about fictional creatures, just that these arguments don't entirely follow.
Maybe I didn't articulate my arguments well enough. I'll try again:
The games repeatedly try to manufacture a moral dilemma where you're given a binary choice between curing the genophage or condemning the krogan to extinction. The dilemma being based on the assumption that krogans are inherently predisposed to breeding out of control. It's a disturbing neo-malthusian space man's burden type of deal that wouldn't be out of place in a Tom Kratman novel.
The logistics as described don't work. The krogans aren't biologically feasible. In fact, any population control dilemma like this doesn't seem feasible.
I'll describe this using the "r/K selection theory." It's been discredited but it's still a useful shorthand.
Essentially, a r-selected species produces a lot of offspring and invests zero parental care because most of those offspring won't live to reproduce. By contrast, a K-selected species produces a small number of offspring and invests parental care to ensure most live to reproduce.
With me so far?
The krogan are described as an r-selected species. The problem here is that it isn't feasible for an r-selected species to develop near-human intelligence. Why? Because things like language and culture and science need to be taught. The krogan should never have been able to develop sapience without a K-selection strategy.
Although the krogan are repeatedly claimed to be an r-selected species, what little we actually do see of their child-rearing practices does resemble a K-selected species. That is, they raise a small number of offspring who they instruct in language, culture and science. At the end of
Mass Effect 3, we see a slide in which a krogan couple hold a baby after the genophage is cured. One baby, not a thousand.
It isn't physically possible for krogans to lay ~1000 eggs per year as they are stated to. An adult krogan is about 8 feet or so tall. A krogan newborn is about 2 feet tall. It isn't physically possible for a krogan woman to pop out a thousand of those two foot babies through her vagina every year, or approximately three births per day.
The writing contradicts itself depending on whether it wants you to be sympathetic toward the krogan or not. It rarely provides hard numbers but when it does those numbers are blatantly absurd.
I don't understand how this is so difficult to understand. The writers tried to pose a neo-malthusian population control dilemma. The problem is that the dilemma is physically impossible and relies on the player having no knowledge of the biological and mathematical science that it butchers.