Laser-induced particle accelerators have been recognized as a potential proton source for radiotherapeutic applications in recent years. However, there are still major difficulties—especially regarding the resulting proton spectra—to overcome for a successful application in the clinic. Here we elaborate on the physics of double-layer targets to propose a tentative 'optical gantry' setup. The spectral requirements for a quality dose deposition of the fast protons are estimated. Plasma simulations of the one-dimensional expansion of microstructured targets are performed according to various target dimensions, rear proton densities and substrate masses. Subsequently, the dependence of the resulting proton spectra on these parameters is evaluated and compared to previously published analytical considerations. Quasi-monoenergetic proton beams, which would be suitable for high-quality dose delivery, could be achieved from pure proton targets if one were able to select out the rear layer of those targets. However, much more realistic heavy substrate layered targets are not able to preserve this high spectral standard, partly due to a second Coulomb-expansion in the center-of-mass frame of the fast protons. This expansion can be mitigated by a reduction of the total positive charge in the rear layer, resulting in a comparable spectral quality as the previous target types. In conclusion, the promising spectral results as well as an estimation of the total number of fast protons which can be expected from such a setup, suggest that the introduction of laser-based proton accelerators into the clinic might be possible in the future.