Quick Answer: a Succor Punch is generally not used to kill/treat/zap parasites, at least not in the conventional sense. The conventional sense: a person applies Zapper electrodes to their body for the purpose of treating/killing parasites. If you really really want to get closer to "why use a Succor Punch?", then you may very likely need to be willing to go relatively far down a particular rabbit hole, such as the kinds and depths of rabbit holes Don Croft frequently chronicles having gone down himself. This particular rabbit hole gets further away from the issue of dealing with parasites directly on and in one's body while getting closer to the kinds of parasites that have long been pulling the various strings and pushing the various buttons animating the world on earth as we - loosley speaking, generally know it.
Look at it this way. In general, a Zapper is also known loosley as a Pulser, a pulser that generates _____ pulses per second, be it 30,000 pulses per second via the classic Clark style Zapper, or 1000 pulses per second via a newer/different design, or 15 pulses per second via the Terminator design. In other words, it's fair to say that Hulda Clark designed a pulser originally designed with the intention of applying the pulsing directly to the human body by use of electrodes IE> "hand holds". Use of this term "pulser" can lead to confusion depending on the people who may be discussing it.
The reason why most if not all trails (found while searching the web for Succor Punch) leads to Don Croft is that he is generally given credit for having invented the SP, which really is just the marriage ... or different application of joining a "pulser" to a combined crystal/moebius. In this case, Don chose to use a pulser (in particular his Terminator style zapper) to power the combined moebius/crystal, then called the resultant "thing" a Succor Punch. As far as an SP being an "esoteric device", I would not argue this point either way (pro or con) any more than I would argue either way many many other things/aspects/devices present in this world; I'm personally not in the position of being well informed enough that I feel comfortable in making a conclusive statement either way. BTW, Don Croft sort of started out as a provider of a tweaked Zapper design. He took Hulda's basic design, added a few things to it, lowered the frequency to 15 cycles per second, built it into a very small and compact enclosure, and used two pennies as the electrodes, one of which bares the portrait of QEII - a multi-pronged message from Don. It was several years after the fact of designing the Terminator that Don would eventually come to marry it to a crystal/moebius and use for "other" purposes.