Because it captures important truths about the physics and gets the right answer; all using just high-school mathematics and very little quantum mechanics. Th

Because it captures important truths about the physics and gets the right answer; all using just high-school mathematics and very little quantum mechanics. The electron really is a wave-like thing confined a by coulomb potential and thus has a discrete set of solutions. Moreover the discrete indexes of that solution map onto mechanical properties like angular momentum and energy. The Bohr model captures all of that, and even gets the right equations for the energy (at least in simple cases). Of course the real wave equation that needs solving is much more complicated than the 1-d cartoon in the Bohr model, but that cartoon works because it captures many essential properties of the real system.