@gratefulcheese I’m way late to the party here, but I believe it also has to do with keeping the root (first note) of the chord in the bass (lowest-sounding tone) when you play the chord.
For example, for an A-major chord, the preference might be to have the lowest-sounding note be the root note (A), in which case you wouldn’t play the low E string, because if you did, your bass/lowest note would be an E, not an A. But since E is actually IN an A-major chord (which consists of A, C#, and E), it still sounds perfectly fine if you do play it!
Same with the other example, D-major. If you skip the first two strings, you’ll then be strumming the chord with the lowest tone being the root (D). If you DON’T mute the A string, that’s okay too, because the note A is in a D chord (D-F#-A). But there’s definitely NOT an E in a D-major chord, so don’t play that string! But your ear will tell you that.
Now, what the actual technique/strategy is behind keeping the root in the bass when strumming, I do not know. Maybe someone can answer that… is it a matter of clarity or something? Or perhaps it’s just to reinforce which note is the root in your brain, for when you’re alternately picking and strumming… or walking up or down to a root note, like in this lesson?