If you ever get a chance to land in a wheat stubble field or a strip with fairly long grass, you'll notice rapid deceleration when you touch down. Grass and stubble offer an awful lot of drag compared to short grass or pavement, and that drag gets much worse as speed increases on takeoff. You might reach a point where the airplane simply won't accelerate any more, so takeoff with a bunch of flap is the only way out of places like that. Get the wheels off even with the horn blaring, accelerate in ground effect, climb away.
When I was an instructor I was amazed at how many PPLs I ran into that had never been off the pavement.
As far as trim with flaps: Flaps move the center of pressure aft a bit, causing a nose-down tendency. But plenty of airplanes have a geometry that causes a pitch-up as the flap downwash strikes the stab. C172 is a classic example. My old Auster 6 had a trim tab on each elevator; one was driven by the trim crank and the other was controlled by the flap control system. Pulling flaps down moved that tab and it completely cancelled any pitch change. It was handy and simple, and yet I've never seen any other aircraft like that.
The Maule M4 has a trim tab on the rudder that is controlled only by the aileron control system, and it works to counter adverse yaw.