Earthquake finite‐source inversions provide us with a window into earthquake dynamics and physics. Unfortunately, rise time, an important source parameter that describes the local slip duration, is still quite poorly resolved. This may be at least partly due to sparsity of currently available seismic networks, which have average sensor spacing of a few tens of kilometers at best. However, next generation observation systems could increase the density of sensing by orders of magnitude. Here, we explore whether such dense networks would improve the resolution of the rise time in idealized scenarios. We consider steady‐state pulselike ruptures with spatially uniform slip, rise time, and rupture speed and either Haskell or Yoffe slip‐rate function on a vertical strike‐slip fault. Synthetic data for various network spacings are generated by forward wave propagation simulations, and then source inversions are carried out using that data. The inversions use a nonparametric linear inversion method that does not impose any restrictions on rupture complexity, rupture velocity, or rise time. We show that rupture velocity is an important factor in determining the rise‐time resolution. For sub‐Rayleigh rupture speeds, there is a characteristic length related to the decay of the wavefield away from the fault that depends on rupture speed and rise time such that only networks with smaller station spacings can adequately resolve the rise time. For supershear ruptures, the wavefield contains homogeneous S waves the decay of which is much slower, and an adequate resolution of the rise time can be achieved for all station spacings considered in this study (up to few tens of kilometers). Finally, we find that even if dense measurements come at the expense of large noise (e.g., 1 cm/s noise for space‐based optical systems), the conclusions on the performance of dense networks still hold.