Your own comment to me illustrates why some sort of space is better. In fact, I can't tell if you're being ironic or not.

Your post is difficult to read because the em dash looks the same as the hyphen later in the post.

The argument that clinches it for me is editing. If you use an em dash with most word processing programs, you will consistently run into problems with the dash and surrounding text being treated as single words. You could reprogram things to recognize em dashes in those scenarios, but the standard behavior exists because of the way the vast majority of people perceive text.

Personally, I think the solution is a thin space, or to drop em dashes in favor of en dashes or something.

I use em dashes frequently, and these issues are frustrating to me. It's also frustrating translating them to plain text.

Depends on typography traditions. In Russian, em-dash in the middle of a sentence is always typeset with short spaces. We also rarely use en-dashes (I think there are maybe two cases when it is allowed: in date ranges like 1940–1945 and as a bullet point in lists).

The space is conventional in Britain. Without the space looks strange to me.

(Android users — try long pressing the - key in the punctuation menu.)

In my opinion — and let's face it, much of this is just a matter of opinion! — a normal space is too much. Try thin space (U+2009) for a more subtle effect. (The exact result may depend on your font, however.)

This was the typographical choice that Medium landed on for their rich text editor as well

I agree; it is down to opinion. I'd like to make use of the thin-space — but it doesn't make much difference in the typeface I'm using to write this reply.

I disagree [1]; pick up a book that's been typeset, and look for an em dash. I doubt you'll see any spaces.

[1] https://en.oxforddictionaries.com/grammar/dash-and-em-dash

When the dash (whatever type) is used to separate parts of a sentence, in British use there will be spaces either side. If Oxford is the exception, then I'm not surprised – they're the exception to many British writing styles. Admittedly, these examples look closer to en than em length.

From some books and a magazine on my table: https://imgur.com/a/GNl2p