1: Why are the elements of a basis set taken to be orthogonal? But in real sense atomic orbitals do overlap.
The number of basis functions involved in heavy atom electronic structure calculations are small compared to those needed for proteins. The smallest known protein has about 45 residues, and a couple of hundred atoms. This results in thousands of basis functions.
Now if you add a transition metal or two, then you've really got a lot. Not only do you have to compute a lot of integrals, but you have to form and diagonalize the Fock matrix or something like it.
Post-HF treatments are needed, in any case, for reliable results, and that's really out there for these systems.