Well, correct me if I'm wrong: you can understand the mechanism by which the chemotherapy acts in the body, but when trying to understand the effectiveness of the treatment you couldn't really isolate the "side effect" from the primary effect in terms of its therapeutic value. Unless you had chemotherapies which were effective despite a lack of those side effects.
You can compare it to more targeted forms of chemo (for a narrow range of cancers) that don't have those side effects, and to surgical procedures. The common thread here being that killing or removing the cells remediates the problem. You can also demonstrate that other things that cause similar side effects don't affect apoptosis (programmed cell death).
I mean, it isn't like researchers pull these ideas out of thin air. Some forms of cancer are more thoroughly researched than just about any other topic in medicine.