Earlier quoted context omitted.
Minor quibble: having a non-integral “number” of spaces was not a TeX innovation; Knuth was just reproducing standard practice of fine typography. Using variable-width separators (TeX “glue”) is exactly how human typesetters did it for centuries. So it's not quite the right perspective to consider anything “a holdover from the typewriter era”, because that had never been typographical practice in the first place — in…
> with TeX's standard settings, the inter-sentence space has the same natural width as the inter-word space That's not quite accurate; the inter-sentence space does have a slightly larger natural width as well as more stretchability. It's right there in Chapter 12 of The TeXbook: > "Plain TeX puts extra space at the end of a sentence; furthermore, it automatically increases the stretchability (and decreases the shrin…
• inter-word space has natural width 3.33333pt, stretchability 1.66666, shrinkability 1.11111.
• inter-sentence space has natural width 4.44444pt, stretchability 4.99997, shrinkability 0.37036.
So the net-effect is that, for example:
• for a line set at natural width: inter-word space is 3.33333pt and inter-sentence space is 4.44444pt (so it's 33% larger)
• for a loose line, stretched by ∛2 (badness 200, the maximum without complaining with the default setting of \tolerance): inter-word space is 5.43319pt, inter-sentence space is 10.7440pt (so it's 97% larger)
• for a tight line, shrunk by ∛2 (badness 200, the maximum without complaining with the default setting of \tolerance): inter-word space is 1.93342pt, inter-sentence space is 3.97782pt (so it's 106% larger)
So only for very loose or tight lines does the inter-sentence space get close to "two spaces".