In the standard Λ cold dark matter (ΛCDM) cosmology, galaxies grow through smooth accretion and hierarchical mergers. While this framework explains many large-scale structures, the existence of massive disc galaxies without prominent bulges-pure discs-remains a challenge. In this work, we investigate the physical origin of the scatter in the stellar mass─size relation of massive spiral galaxies, with a particular focus on bulgeless systems. Studying these systems is also key to understanding the evolutionary history of our own Galaxy, the Milky Way, which is known to host a low-mass bulge. We performed a structural analysis of 22 nearby bulgeless galaxies from the Bulgeless Evolution And the Rise of Discs (BEARD) survey. To minimise the scatter in the stellar mass─size relation, we adopted a proxy for the physically motivated definition for the galaxy size, based on the radius R1, where the stellar mass surface density reaches Σ* = 1 M⊙ pc−2. For this purpose, we used deep g- and r-band imaging obtained with the 2.5 m Isaac Newton Telescope-Wide Field Camera. We derived surface brightness, colour, and stellar mass density radial profiles, which allowed us to obtain precise measurements of R1. Point spread function (PSF) effects were corrected through star subtraction and wavelet deconvolution. BEARD bulgeless galaxies follow the tight stellar mass─R1 relation defined in previous studies with a similar scatter (∼0.1 dex). We also constructed the same relation using galaxies from the IllustrisTNG50 simulation. We find a morphological segregation contributing to the scatter of the relation, with bulgeless (BEARD-like analogues) and bulge-dominated galaxies defining the upper and lower envelope, respectively. We find that this morphological trend shown by the simulations is strongly correlated with the specific central stellar mass density, Σspec1,kpc Σ 1 , kpc spec , defined as the stellar mass surface density enclosed within the central kiloparsec, normalised using the total galaxy mass. The observed discrepancy between observations and simulations can be attributed to the broader Σspec1,kpc Σ 1 , kpc spec distribution covered by our observed BEARD bulgeless galaxies. A deeper analysis of the physical driver of this morphological segregation reveals that the scatter in the mass─size relation is also related to the spatial configuration of merger events, rather than their frequency, with bulgeless systems tending to inhabit halos with a slightly higher spin.