But then you can't verify your altimeter's accuracy when crossing the FAF.

Only if the GPS goes TU - otherwise the GPS will give you at least as
good a fix as a cross-radial. What are the odds you lose the GPS and
the altimeter goes wonky at the same time? In low IMC? In a minimally
equipped C172? Really think it's worth raising the workload at FAF
intercept for that? I sure don't. Then again, I don't time my ILS
approaches either.

Michael