One of the pieces, The apostrophe: A neglected and misunderstood reading aid, has this to say:
Almost all apostrophes commonly explained as indicating omission can also be explained as marking morpheme boundaries. No apostrophes that do not mark boundaries do occur at all in the earliest texts and in modern formal texts.
Consequently, the apostrophe ought to be defined as having as its one dominant function the indication of morpheme boundaries where for certain reasons this seems necessary….
Furthermore, the apostrophe, which was borrowed into the Latin alphabet from Greek, seems to have indicated a boundary rather than an omission from the start.
This is also how apostrophes are used in Pinyin.