(I started to write this before the other answer was posted, but could not finish it earlier, so I'm posting it anyway. The other answer is good and I have upvoted it.)
I think one of the reasons why we don't have a vast array of font sizes and colours available for editing questions is to try and keep some consistency across the site.
In line with that, the vertical spaces between paragraph also helps consistency across the site, so IMHO, it makes sense to remove the white space as you did. However, yes, I think replacing those empty paragraphs with horizontal lines would have helped keep the logical separation of thoughts.
Did I overstep my bounds by editing out the extra whitespace?
I don't think so.
Should I have added a horizontal rule to maintain the intended separation with less vertical space?
I think so.
Should I have left the question as-is?
I don't think there is a should or should not here. You think you improved the post to make it easier to read, and that's what we expect when the posts are edited.
A note about horizontal lines.
I find them useful to separate a post with multiple aspects to them, like...
A conclusion, or a set of notes or references.
But they can be annoying if they're over used.
Alternatives exist when you want to add variety:
Heh... another type of title....
Titles with dashes
Bold stuff on its own line
(with the continuing text...)
You get the idea...
More information about these alternatives is available in the
Markdown Editing Help or the subsequent