You're not wrong. That is distressing.

I cant watch the video now, but the British version is a bit like that:

A B C D E F G

H I J K L M N

O P Q

R S T

U V W X Y Z

Yes it doesn't rhyme but it scans so much better that, once you're used to it, the American NLMOP version sounds ridiculous.

The LMNOP is just rhythmic variations: you have a run of 16th notes.

Such a pattern of 16ths occurs in "have you any wool" in the English nursery rhyme "Baa Baa Black Sheep", which is sung to the same tune.

I agree that sort of flourish is a lot of fun, if it's not in a song trying to teach you something so fundamental.