“Take the lead” is certainly an expression used in the UK to denote guiding people, as in “I’ll take the lead”. I assume both come from ballroom dancing.

I’m sure it’s used elsewhere but it may also simply be a conflation of the two.

Very much so - it’s why I came into the comments.

Unfortunately, you violated the law slightly by asking a question!

Cunningham’s Law states “the best way to get the right answer on the internet is not to ask a question; it’s to post the wrong answer.”

I think you’re underestimating the intelligence of average people. There’s definitely a lack of knowledge, but average people are plenty smart to invent everything you’ve listed. It just takes time and is an iterative process.