The ground-state properties of the S = 1/2 transverse-field Ising model on the checkerboard lattice are studied using linear spin-wave theory. We consider the general case of different couplings between nearest neighbors (J(1)) and next-to-nearest neighbors (J(2)). In zero field, the system displays a large degeneracy of the ground state, which is exponential in the system size (for J(1) = J(2)) or in the system's linear dimensions (for J(2) > J(1)). Quantum fluctuations induced by a transverse field are found to be unable to lift this degeneracy in favor of a classically ordered state at the harmonic level. This remarkable fact suggests that a quantum-disordered ground state can be instead promoted when nonlinear fluctuations are accounted for, in agreement with existing results for the isotropic case J(1) = J(2). Moreover, spin-wave theory shows sizable regions of instability, which are further candidates for quantum-disordered behavior.