I don't really agree that properly made pads massively change the frequency response.
I think what you're probably disagreeing on is the definition of the term "massive." As it is a subjective term that is relative to the individual perception.
However, I would disagree that the changes cannot be "significant," which has been Amir's claim.
For example, when increasing bass with pads, one is doing so without getting closer to the distortion limits of the driver as similar EQ boost would do. Which could be advantageous for those who listen loud or like a lot of bass. That can also be helpful when desiring more bass when using more difficult to drive headphones with mobile devices that don't have a lot of amp headroom.
Some pads have been shown to decrease peaks and/or reduce dips to smooth the response. Which always seems an advantage to me over having to use EQ to do it.
And while we have not been addressing it since the discussion has been centered on frequency response, pad changes can increase isolation.
Finally, whenever those characteristics are coupled with a more comfortable pad change, it's a big win.