Is the dot a period at the end of a sentence? In that case, there should be an m-space following the period, and line breaks are allowed after the period. Is the dot an abbreviation of an honorific (e.g. Mr. So-and-so)? In that case, there should only be an n-space, and line breaks between the honorific and the name should be forbidden. Is the dot an abbreviation of a unit (e.g. 3 lb.)? In that case, the period may or may not also indicate the end of a sentence, and should have an m-space or n-space depending on which it is.
While I think the typesetting software should be smart enough to distinguish these cases on its own, like LaTeX does, the parent's point is that the user can add extra information in the form of double spacing to indicate what length of space is appropriate.
It's not a matter of choosing what the period does. It's a matter of codifying what it already does. Certainly, you can treat "3 lbs." as a regular word. That is another use case for a period, which also needs to be handled. That also means that a period can either appear inside a word, or between words.
The long story is that a period can mean many, many different things.
Except that in the tradition current when I was growing up neither Mr nor St require a dot because they both include the last letter of the word. The dot is meant to indicate that letters following it have been omitted.
This is a key punctuation difference between North American and UK English. In NA, we use the dot here, but not in the UK. Actually, I’ve started to adopt the UK convention, because I think it looks neater.
Meanwhile, the house style at the NYT is to use periods between each letter of an acronym in certain cases, e.g. W.H.O., D.O.D, and U.N., but not NASA for some reason.
I've had to occasionally append to existing texts that use the period between each letter style, and I have to say, it's incredibly annoying to physically type.
"..." shouldn't be used for ellipses; the spacing is bad. That's why we have the single "…". (Maybe we need code points for "SENTENCE-ENDING PERIOD" and "NON-SENTENCE-ENDING PERIOD"?)
They just don't get it, and perhaps won't understand the problem until it kicks them in the shin.
The appropriate counterattack might be to introduce some coding and just show how gnarly sentences are to process as a result.