Of course Earth must have some finite carrying capacity, but that's only terrifying if you assume that "The Crunch" is the only way to bring population growth to a halt.

Population growth is already zero or negative in most developed countries if you remove the effects of immigration. If this becomes a consistent rule for all countries once they become fully developed, the real question is not whether we can sustain infinite population growth, but whether we have the resources to support a developed lifestyle for the entire world. Given current technologies and energy sources, the answer is almost certainly "no", but this is a much more tractable problem.