Back in the dark ages, when I was first learning to type, the Word of God as passed down from on high by the instructor (who was more interested in training 80-words-a-minute secretaries than in teaching the rudiments of touch typing to a future English major) was that you double-spaced following a period.
I never became an 80-words-a-minute typist, but those two spaces after the period were hardwired into my brain, not to mention into my spacebar-hitting thumb.
Cue the musical montage representing the passage of time, with the tappity-tappity-tappity-bing! of the typewriter fading into the musical-popcorn boop-boop-boop of the old computer keyboards, and that sound fading in turn into the near-silence of keyboards today . . . followed by the Word of God saying that it is now customary to space only once after a period.
Why is this something it doesn’t pay to worry about? Because, one, of all the reasons an editor may have for rejecting your manuscript, the question of how many spaces you’ve put after your periods is way low on the list. And, two, if the whole thing bothers you that much, you don’t have to sweat blood retraining your spacebar thumb — all you have to do is run a search and replace during the final edit, and change every instance of two spaces to a single space instead.
Dr. Doyle's Blog 
The two-spaces-after-a-period is the last remnant of the entire American Spacing/English Spacing/Continental Spacing styles.
As you say, I doubt the agent or editor breathes who’d say “Your story is fresh, vital, compelling! But you double-spaced after the periods so, alas, we must reject this piece.”
(Note: There exist certain bottom-feeding “publishers” who go into great detail on exactly how a manuscript is to be formatted; this is because they will dump the raw manuscript into a template after performing a minimum of work (NOTE: the minimum may include cashing a check; it doesn’t include actually reading the story) and voila! a book! Which you can buy from them at inflated prices to sell from the trunk of your car, or that can languish forever in digital form at Amazon.com while you repeatedly tweet its URL. I would not consider such a publisher.)
Well, that’s the difference between working with a monospaced font and a porportional font. The computer effectively adds the extra spacing for you automatically.
And, yeah, it isn’t worth worrying about.