Are ionic bonds stronger than covalent bonds?
In a fully covalent bond, you only have the mixing of the orbitals, as you said. But it's not only that, you also have coulomb interactions between the nuclei, that slightly raise the energy of the molecular orbitals, which results in asymmetric energies.

In a fully ionic bond you also have a coulomb interaction, but this time with the different sign, because you have a positive and a negative charge. These want to be as close together as possible, resulting in a stronger bond.

Generally speaking: Coulomb interactions have a greater impact than molecular orbitals on the energy, and thus the strength, of a bond.

It's almost like saying that electromagnetic forces are stronger than gravitational forces.