The entire point of that whole battle is to encourage Harry to commit his hidden resources (Lesath under the Cloak). The whole brawl is basically a show put on for Harry's benefit. Since Quirrell controls the time of Harry's coming to the scene, he could easily take out Snape himself and move him out of the way earlier. He didn't need to bring Sprout or manipulate others to come.

Since Quirrell neglected to ask Harry in Parseltongue whether he still has hidden resources Quirrell doesn't know about, it's still just about possible that Cedric Diggory, Time-Turned, is following them under the second Cloak. I hope he does.