"Cannot possibly" is a very limiting statement you've made.
In a typical one- to two-hour first lesson, my students increase their APA handicaps two points. They consistently tell me weeks after they've been winning all or nearly all their matches and were put up by league bosses two points. I frequently get a call or email a few weeks after even a first intensive lesson.
I've had a C player become a shortstop, his dream, after ten hourlong lessons, a week or two apart each. I've had players fly me in for a weekend to improve in local leagues but then quit their leagues to play in pro-ams, etc.
Because TK is a good friend and other reasons, we are adding a lot of "secret sauce" to this clinic and a player could well/easily go up from C to B or B to A. My speciality isn't "Let me change your grip, stance and stroke, now practice for six months two hours a day to improve," it's far more often "You have a great grip, stance and stroke," let me show you how to do those in a pro manner and you will become much stronger BEFORE THIS LESSON ENDS.
While I've had students tell me I have ideas that seem to come from outer space, I pledge that anyone's pocketing ability and position play will dramatically increase in a single lesson or money is returned.
There are some teachers who are very diligent and will not end the lesson until their student is significantly better. Unfortunately, in my (limited) experience most teachers make radical changes to a student's fundamentals than are pleased when they improve after two hours a day practice for six months.