These planes typically pull out of a dive on their own, but then climb excessively and stall, leading to another dive.
R/C flying can be started at an early age and gives any potential pilot a huge head start in gaining experience in the all important fundamentals of flight.
A lesson in the importance of keeping CG within the specified range (and the consequences of not) is better learned at model, rather than full scale.
Not paying attention to aft CG limits (weight too far back) will reduce directional stability in pitch and yaw. It will roll 360 beautifully, but only because the tail will constantly try to drop throughout the roll, always raising the nose. In general the aircraft will be more maneuverable, but harder to control. (This is why modern military aircraft use computers to assist stability).
Among the plethora of bad things (such as stalling low and slow) that can happen, dynamic instability is another consequence of out of range CG. Especially with models, a fraction of an inch can matter.
But if you build from scratch, it is important to properly match the tail and wing. Amazingly, a horizontal "stabilizer" destabilizes pitch when a plane rises or sinks vertically. This is a very important aspect of static stability.
Rising or sinking vertically is a function of lift. Therefor, excessive lift can cause a plane to "overshoot" its correction to original flight path. An extreme example of this is a loop.
So we generally design the wing Center of Pressure to be aft of the Center of Gravity so the torque of the wing lift around the center of gravity helps control the pitching tendency when lift is increased.
The further back the center of gravity, the greater the pitching tendency will be.
For custom scratch builders, a larger tail or longer tail moment is an option, but remember, if the tail supports weight, you are essentially building a bi-plane.