I have not read the book because I loaned it out and haven’t gotten it back, but I was surprised that Kyle took on the house-to-house duties, as well. He truly led by example.
I just watched it.
As a former Marine, that surprised me too.
I can't imagine ANY US Marine Squad Leader or Fireteam Leader undergoing a combat mission allowing a Navy Seal to commandeer his squad in order to "teach" them how to clear houses.
If this is, in fact, in the book, I'll have to chalk it up to literary license as he used in punching out Jesse Ventura in the bar.
Otherwise, I'll chalk that up as "Hollywood".