Have you noticed that when you are in an airliner, and it banks into a turn, that the liquid in your drink stays parallel to the floor, and other than a sensation of maybe rolling a bit, you can't tell you're in a turn if you can't see outside? In a maneuvering airplane, centrifugal forces from turning, and gravity, create a net force that is always perpendicular to the floor. So the "down" you feel is always down relative to the airplane's floor, not relative to the real "down", the ground below.
A physical inclinometer like you describe won't work while moving because of those forces, unless the airplane is skidding sideways, which it normally isn't. Airplanes actually use such an inclinometer, but it's used for detecting that skidding motion, which is bad to have because flying sideways is inefficient.
The only thing that can indicate where the earth actually is, while the airplane is moving around, is a gyro, so instruments that indicate bank and pitch angles, by presenting a virtual horizon for the pilot to use when he/she can't see outside, depend on gyros, either mechanical or electronic (using lasers).
The struggle for the pilot is the conflict that occurs in the inner ear when it senses motions that aren't being confirmed by the visual picture (an outside horizon) except for the instrument indications. Unless well trained to ignore your head and trust the instruments you see with your eyes totally, you get dizzy and disoriented, and it can get so bad that you lose control, like what happened to Kennedy.