Yeah, even the modified chain breaker that I fashioned into a cotter press has needed a few additional rounds of grinding over the years to fit every crank that I've come across, but it's no big deal to hit it with the bench grinder as needed. Heck, I remember having to grind the heck out of that casting to use it even for the first time!
If the cupped driver can't fully self-center on the cotter, the cotter will tend to fold over under full force of cotter removal. Removing metal as needed to clear the spider is just an adjustment that expands the range of cranks you can service with the tool.