Vegetal and mineral fibres are the newest Textile Reinforced Mortar (TRM) systems group entries. The inherent differences these meshes show compared to the “classical” synthetic ones, such as lower elasticity modulus and the notable reinforcement ratios, raise concerns regarding the applicability of conventional testing and modelling. To investigate to what extent the standard bond-slip model can tackle the response of low-modulus fibre systems, i.e., vegetal and mineral-based, failure domains are defined and compared through parametric investigation of geometrical, physical and mechanical characteristics. After defining the thresholds for architectural reinforcement properties and identifying different Natural TRM (NTRM) typologies, the local slip, strain, and shear stress functions are provided in closed form for various boundary conditions. Then, debonding failure domains are built, considering continuous variations of the main parameters characterising the system’s response, such as the axial stiffness and the Cohesive Material Law (CML) characteristics. As the required embedded length of the NTRMs depends on the CML, the testing length for systems with lower elasticity modulus and greater equivalent thicknesses requires careful design to ensure the bond behaviour at the reinforcement-to-mortar interface development, fully exploiting the composite materials’ mechanical parameters.