The AKARI IRC all-sky survey provided more than twenty thousand thermal infrared observations of over five thousand asteroids. Diameters and albedos were obtained by fitting an empirically calibrated version of the standard thermal model to these data. After the publication of the flux catalogue in October 2016, our aim here is to present the AKARI IRC all-sky survey data and discuss valuable scientific applications in the field of small body physical properties studies. As an example, we update the catalogue of asteroid diameters and albedos based on AKARI using the near-Earth asteroid thermal model (NEATM). We fit the NEATM to derive asteroid diameters and, whenever possible, infrared beaming parameters. We fit groups of observations taken for the same object at different epochs of the survey separately, so we compute more than one diameter for approximately half of the catalogue. We obtained a total of 8097 diameters and albedos for 5170 asteroids, and we fitted the beaming parameter for almost two thousand of them. When it was not possible to fit the beaming parameter, we used a straight line fit to our sample's beaming parameter-versus-phase angle plot to set the default value for each fit individually instead of using a single average value. Our diameters agree with stellar-occultation-based diameters well within the accuracy expected for the model. They also match the previous AKARI-based catalogue at phase angles lower than 50{deg}, but we find a systematic deviation at higher phase angles, at which near-Earth and Mars-crossing asteroids were observed. The AKARI IRC All-sky survey is an essential source of information about asteroids, especially the large ones, since, it provides observations at different observation geometries, rotational coverages and aspect angles. For example, by comparing in more detail a few asteroids for which dimensions were derived from occultations, we discuss how the multiple observations per object may already provide three-dimensional information about elongated objects even based on an idealised model like the NEATM. Finally, we enumerate additional expected applications for more complex models, especially in combination with other catalogues.