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.
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.