Most airplanes have the wing at an angle relative to the fuselage. The reason is that most are designed for a single mission. That mission requires a wng design lifting a certain amount. For instance a 747. Lots of flying at a cruise speed. At that wing angle of attack you want the fuselage to have the lowest drag. This is usually with the fuselage at a zero angle of attack but which is optimized in the wind tunnel tests.

The only exceptions that I am aware of are the control line stunt and combat (maybe speed) and RC aerobatic, stunt, combat types.

The F-15 can't really be said to have the wing at an angle relative to the fuselage (incidence angle) since the airfoils, camber, and twist vary all the way out to the wingtip and also vary in flight with loads. When we were in the initial design of the airplane (I was a member of the aero dept that designed the airplane and worked on and off with it for over 20 years) one of the baseline wings we took data on (you need to start somewhere) was an untwisted, uncambered, mostly symmetrical airfoil. That one could be said to have an incidence angle with reasonable meanings.

The F-15 also has such a wide range in flight conditions it is difficult to optimize an incidence angle, do you optimize it to do loiter or range or combat. It becomes a question of how many balls you can juggle to come up with the answer.

Also keep in mind that lift doesn't come from thrust, rockets and the Harrier do that. You need forward velocity which can come from thrust or gravity (remember gliders).

-------------- The idea is that there should be no lift-induced moment around the center of gravity when the plane is flying, otherwise it'll keep pitching up or down.----------------

Correct

As far as the physics being simple -- my friends with Doctorates in the field might disagree :-)