We show that in generic single field inflation models, an axial coupling of the inflaton to electromagnetism generates always the same spectrum of helical magnetic field fluctuations. We trace the evolution of the magnetic field distribution through the turbulent plasma epoch after inflation. An inverse cascade takes place that moves power from small to large scales. However, this process is not efficient enough to overcome the bound from not allowing the magnetic fields to backreact onto the inflaton dynamics. Therefore, the magnetic fields produced in this scenario are not sufficiently strong to provide the seeds for the magnetic fields observed in cosmic structures and the intergalactic medium.