Certainly true that more horizontal spacing between sentences is good for readability. Certainly false that hitting the spacebar twice, like a caveman, is the way to achieve this.
Exactly. A good typesetting system will leave more inter-sentence space than inter-word spacing, but this has nothing to do with the number of ASCII 0x20 symbols after the full stop (period) at the end of the sentence.
But what typesetting system has a way of marking up sentence endings? Because you can rely on the period being that as e.g. this sentence has one in the middle of the sentence.
LaTeX does. The general rule it uses is that a period followed by a space marks the end of a sentence. To mark an intra-sentence period, a backslash is used between the period and the space.