We apply a versatile variant of orbital-free density functional theory, density-potential functional theory (DPFT), to atoms, molecules, solids, and quantum gases. Interacting many-body systems with large particle numbers like quantum gases or solid states with long-range interactions in various dimensions pose formidable challenges even to state-of-the-art theoretical methods. We use recently developed systematic semiclassical approximations of energies and particle densities to describe concrete interacting fermion systems. By design the single-particle densities employed here can be improved systematically beyond the Thomas-Fermi approximation and can be used for efficiently addressing inhomogeneous interacting systems due to the favorable quasi-linear (even sublinear for some systems) scaling of DPFT with particle number. DPFT yields self-consistent interacting particle densities in a spirit similar to the Kohn-Sham scheme, but circumvents the need for orbitals and does not require an explicit density functional for the kinetic energy. These features put DPFT in the position to become a real alternative to established many-body techniques, and here we showcase a number of its real-world applications.