The ongoing development of electromagnets based on high temperature superconductors has led to the conceptual exploration of high-magnetic-field fusion reactors of the tokamak type, operating at on-axis fields above 10 T. In this work we explore the consequences of the potential future availability of high-field three-dimensional electromagnets on the physics design point of a stellarator reactor. We find that, when an increase in the magnetic field strength B is used to maximally reduce the device linear size R ∼ B−4/3 (with otherwise fixed magnetic geometry), the physics design point is largely independent of the chosen field strength/device size. A similar degree of optimization is to be imposed on the magnetohydrodynamic, transport and fast ion confinement properties of the magnetic configuration of that family of reactor design points. Additionally, we show that the family shares an invariant operation map of fusion power output as a function of the auxiliary power and relative density variation. The effects of magnetic field over-engineering and the R(B) scaling of design points with constant neutron wall loading are also inspected. In this study we use geometric parameters characteristic of the helical axis advanced stellarator reactor, but most results apply to other stellarator configurations.