http://acko.net/blog/zero-to-sixty-in-one-second/
All of their MathBox-powered articles are wonderfull really.
I also tend to use it sometimes despite knowing the gender of the person I am referring to. This seems reasonable to me, because I don't see any reason why it is important to always specify the person's gender, when I don't need to specify who the person is, and doing so allows me to refer to someone without specifying a gender, should any situation occur where that would be useful, without anyone commenting on my word choice, because I would already be in the habit of sometimes leaving it out.
Only to a prescriptivist[1] trying to keep the language static. "Cromulent" is slowly making its way into descriptivist[1] dictionaries and is recognized about as often as any other new word, so it just as much a "real" word as other new words ("email", "google" (transitive verb), "truthiness").
> the correctness of using a singular they
The alternative is gendered pronouns which have several problems[2].
/* I'm not trying to nitpick your post; I just thought these two Tom Scott clips were fun and relevant to these grammar issues. */
Also, the videos you referenced are great :)