Previous studies show that city metrics having to do with growth, productivity, and overall energy consumption scale superlinearly, attributing this to the social nature of cities. Superlinear scaling results in crises called “singularities,” where population and energy demand tend to infinity in a finite amount of time, which must be avoided by ever more frequent “resets” or innovations that postpone the system’s collapse. Here, we place the emergence of cities and technological civilizations in the context of major evolutionary transitions. With this perspective, we hypothesize that once a planetary civilization transitions into a state that can be described as one virtually connected global city, it will face an “asymptotic burnout,” an ultimate crisis where the singularity-interval timescale becomes smaller than the timescale of innovation. If a civilization develops the capability to understand its own trajectory, it will have a window of time to affect a fundamental change to prioritize long-term homeostasis and well-being over unyielding growth—a consciously induced trajectory change or “homeostatic awakening.” We propose a new resolution to the Fermi paradox: civilizations either collapse from burnout or redirect themselves to prioritizing homeostasis, a state where cosmic expansion is no longer a goal, making them difficult to detect remotely.