We explore the phenomenology of scalar fields coupled to asymptotically safe quantum gravity, in light of their potential significance for dark matter, for the inflaton as well as dynamical dark energy, and in the Higgs sector in and beyond the Standard Model. This work is a step toward delineating the boundaries of the asymptotically safe swampland by exploiting the constraining power of the asymptotic-safety paradigm. First, we strengthen indications that quantum gravitational fluctuations could drive scalar potentials toward flatness, with intriguing potential implications for inflation and dark energy. Second, we explore how asymptotic safety could rule out large parts of the parameter space in models for scalar dark matter. Third, we discover hints that at an asymptotically safe fixed point with finite top quark mass, the nonminimal Higgs-curvature coupling could be constrained. Finally, by combining the constraining power of asymptotic safety in particle physics and cosmology, we find hints that Higgs inflation lies in the asymptotically safe swampland. In summary, we strengthen previous indications for the constraining power of asymptotic safety and the resulting large extent of the asymptotically safe swampland.