Back pressure is a myth. Or at least in that it causes harm by itself.
What actually happens is the exhaust gas speed increases. That creates more pull on the intake air during the overlap period. That sucks more air and fuel out the exhaust. That creates a situation where combustion can keep going during the exhaust phase. This prolonged period of heat then very rapid cooling of the exhaust valve makes them brittle. Over time it can eat away at the valve, which is what a 'burnt valve' is.
It has nothing to do with reflected waves or anything like that that you may find.
Also the situation where a V-8 may burn a valve is different than situations where a V-6 or I-4 could burn a valve.
Far as the MPG drop,
Why would a kid cut a muffler off? To sound cool, right. Well, does it sound cool when just putting around? Not really. So it stands to reason that the kid would be romping on the car, lowering MPG.
Almost all of us did it as kids.
Just make him pay for fuel. He'll figure it out real quick that his driving is costing too much money.
Don't "think outside the box".
There is no box.