This is the basic premise. It is a false premise.
Humans have the unique ability to increase the carrying capacity of the earth.
Humans also have the unique ability to expand their population and life to other places outside of the earth, and to access resources outside of the earth.
It is highly likely the human ability to unlock carbon from where it has been sequestered in the earth's crust,and to increase the amount of fixed nitrogen in the earth's ecosystem, have already increased the carrying capacity of the earth significantly.
The "carrying capacity" of the earth is not a constant.
In engineering, you use an operating envelope to understand systems. You understand where the limits are for a system and do not operate the system above those limits. Aircraft are a good example.
Can the earth support one trillion people? What is the earth’s operating envelope?
In the end, it doesn’t matter how ingenious humans are if they keep reproducing exponentially. The exponential growth from 1800 to today was made possible by human ingenuity. But where will you get the resources to support a trillion people?