WreckRman2 said
The engine just pulls it forward so that the wind over the wings will create the lift to make it fly. Take away that speed and you produce less lift.
and
Remember it's a trainer were talking about here, not a 4lb fun fly that you want to hang on the prop.
Yes, it's true that you don't NEED that prop on a trainer. But you also don't need the airspeed a 6" pitch gives you on a trainer, these aren't racers either
In my experience, most guys do better with a slower moving trainer that can climb away from the ground at a low airspeed than a faster moving plane. And the LT-40 and other good trainers are perfectly capible of flying at the slower speeds, they don't need that high airspeeds to stay in the air. So give the beginner more time to react by flying slower. You can fly slower with a 6" pitch by throttling down. But they you have to throttle up to climb away from the ground. Not a big deal, of course, but if you can slow the plane and maintain the climbing ability, why wouldn't you?
A 12x4 should rev about the same as an 11x6, so the fuel useage would be simular. I agree than an 11x5 might be more RPM than you'd want, with a higher fuel draw and more noise. But I honestly don't think it will be that much higher fuel draw or noise.
On the whole, you might not even notice a difference. You might decide you like the 11x6 better than the 11x5. Or vice versa. Or you might find a totally different prop that suites you and your combination of engine, airframe, air density, fuel etc etc. Heck, just compare a MAS and an APC in the same size on the same plane, there's a noticeable difference right there.
But don't be afraid to try other sizes that aren't listed in the manual. And don't be afraid to try other brands, they perform differently.