I don’t know for sure. I need to read up on Hamiltonians, it appears.

But, it looks like perturbation theory seeks to approximate an entire system/quantity by approximating increasingly small “perturbations” to a known system/quantity. Without doing an expansion on this system before trying to use the perturbation theory, we would not have set the system/quantity up as a sum of a ‘known system/quantity’ and a small perturbation to be estimated. We would just be trying to approximate the whole thing from scratch.