Context. Chemical element transport processes are among the crucial physical processes needed for precise stellar modelling. Atomic diffusion by gravitational settling is usually taken into account, and is essential for helioseismic studies. On the other hand, radiative accelerations are rarely accounted for, act differently on the various chemical elements, and can strongly counteract gravity in some stellar mass domains. The resulting variations in the abundance profiles may significantly affect the structure of the star. Aims. The aim of this study is to determine whether radiative accelerations impact the structure of solar-like oscillating main-sequence stars observed by asteroseismic space missions. Methods. We implemented the calculation of radiative accelerations operating on C, N, O Ne, Na, Mg, Al, Si, S, Ca, and Fe in the CESTAM code using the single-valued parameter method. We built and compared several grids of stellar models including gravitational settling, some with and others without radiative accelerations. We considered masses in the range [0.9, 1.5] M-circle dot and three values of the metallicity around the solar value. For each metallicity we determined the mass range where differences between models due to radiative accelerations exceed the uncertainties of global seismic parameters of the Kepler Legacy sample or expected for PLATO observations. Results. We found that radiative accelerations may not be neglected for stellar masses higher than 1.1 M-circle dot at solar metallicity. The difference in age due to their inclusion in models can reach 9% for the more massive stars of our grids. We estimated that the percentage of the PLATO core program stars whose modelling would require radiative accelerations ranges between 33% and 58% depending on the precision of the seismic data. Conclusions. We conclude that in the context of Kepler, TESS, and PLATO missions which provide (or will provide) high-quality seismic data, radiative accelerations can have a significant effect when properly inferring the properties of solar-like oscillators. This is particularly important for age inferences. However, the net effect for each individual star results from the competition between atomic diffusion including radiative accelerations and other internal transport processes. Rotationally induced transport processes for instance are believed to reduce the effects of atomic diffusion. This will be investigated in a forthcoming companion paper.