The inhomogeneous solar corona is continuously disturbed by transverse MHD waves. In the inhomogeneous environment of coronal flux tubes, these waves are subject to resonant absorption, a physical mechanism of mode conversion in which the wave energy is transferred to the transition boundary with the ambient corona. Recently, transverse MHD waves have also been shown to trigger the Kelvin-Helmholtz instability (KHI) due to the velocity shear flows across the boundary layer, and their continuous driving has been shown to lead to fully turbulent loops. In this work, we show that resonant absorption plays a key role in energising and spreading the transverse wave-induced KHI rolls all over the loop. This is shown by performing simulations of impulsively triggered transverse MHD waves in a loop that initially lacks a boundary layer. In the absence of this layer, the first unstable modes have high azimuthal wavenumber. A boundary layer is generated relatively late due to the mixing process of KHI vortices, which allows the late onset of resonant absorption. As the resonance grows, lower azimuthal wavenumbers become unstable, in what appears as an inverse energy cascade. The velocity shear from the resonance also triggers higher order azimuthal unstable modes radially inwards inside the loop and a self-inducing process of KHI vortices occurs gradually deeper at a steady rate until all the loop is covered by small-scale vortices. We can therefore make the generalisation that all loops with transverse MHD waves become fully turbulent.