High-resolution computer simulations of earthquake sequences in three or even two dimensions pose great demands on time and energy, making lower-cost simplifications a competitive alternative. We systematically study the advantages and limitations of simplifications that eliminate spatial dimensions, from 3D down to 0/1D in quasi-dynamic earthquake sequence models. We demonstrate that, when 2D or 3D models produce quasi-periodic characteristic earthquakes, their behavior is qualitatively similar to lower-dimension models. Certain coseismic characteristics like stress drop and fracture energy are largely controlled by frictional parameters and are thus largely comparable. However, other observations are quantitatively clearly affected by dimension reduction. We find corresponding increases in recurrence interval, coseismic slip, peak slip velocity, and rupture speed. These changes are to a large extend explained by the elimination of velocity-strengthening patches that transmit tectonic loading onto the velocity-weakening fault patch, thereby reducing the interseismic stress rate and enhancing the slip deficit. This explanation is supported by a concise theoretical framework, which explains some of these findings quantitatively and effectively estimates recurrence interval and slip. Through accounting for an equivalent stressing rate at the nucleation size h* into 2/3D models, 0/1D models can also effectively estimate these earthquake cycle parameters. Given the computational efficiency of lower-dimensional models that run more than a million times faster, this paper aims to provide qualitative and quantitative guidance on economical model design and interpretation of modeling studies.