Language has several components and they can be ranked in a hierarchy of rigidness:
Grammar
Spelling
Style
Meaning
Pronunciation
Teachers spend most of their time trying to pound the round rules of grammar into the square heads of pupils. Spelling is sufficiently fixed that we can delegate its operation to automatic spell-checkers. Style is merely a list of a million decisions that we agree to follow. Words accrue new meanings all the time and can even reverse them over history. Pronunciation varies not only between regions but within regions and from moment to moment in any individual’s life.
Yet, there are amazingly long books by grammarians vehemently arguing fine points that 99% of professional writers never heard of and both meaning and pronunciation have enough continuity that we actually manage to understand one another most of the time.
Teachers have to maneuver between these and give students a firm enough foundation that they can be understood and not thought deficient in standard speech. That’s why they mostly say “do it this way.” “This way” may not be perfect but it will be accepted by almost everyone. The use of apostrophes is sometimes spelling, and sometimes grammar, and sometimes style and gets jumbled together because they are thrown into one pot. I suppose it shouldn’t be all that surprising when people dip their forks into the pot of apostrophes and mash possessive and plural together.
But the purpose of teaching it’s/its and their/they’re is to make sure that students understand that they are two pairs of totally different words that merely happen to be pronounced alike. They might as well be yellow/computer or freedom/stapler. Meaning outranks pronunciation. Students are forced to memorize that sound is not important here. A lot of language is plain memorization, because few things can be logicked. The irony is that apostrophe use is one of them.
But inserting “the” implies that John is somehow “the Smith”, which is at least awkward and probably wrong. (Unless he happens to be the sole local blacksmith, knifesmith, etc.)
Well, I’ve met people who actually say they were taught that proper nouns are inviolate and thus take an apostrophe in the plural. And it would seem odd otherwise that this particular grammatical peculiarity pops up so regularly.
Because “the Smiths” is correct for the members of the Smith family. The Smiths live (as you’d expect) in the Smiths’ house.
But “the Smith” is not correct for an individual named Smith. That person could be John Smith or Jane Smith or Mr Smith or Ms Smith or even just Smith, but not the Smith. Consequently the house that person lives in is not the Smith’s house.