Fare enough? not really, I can imagine at least three valid reasons to use those

1) I want to check that my code works for complex builds, even if I have pure real function evaluations. I may need complex support in other parts or the code (not when using TAO), or I just want to be a diligent PETSc developer

2) I want to test REAL gradients or Hessians using built-in capability, instead of writing my own

3) I want to use the complex differentiation trick to compute REAL gradients

Last time I checked, at least option 2) was available; However, from commit 5921d7004dad83427f45468906667b100d2e2b6e, no Tao methods are registered when PETSC_USE_COMPLEX is defined, and code like the one below fail at runtime:

TaoCreate()

TaoSetFromOption()

TaoSetObjectiveRoutine()

TaoTestGradient()