Avor this statement isn't completely true.
In a real fighter, when the plane is pointed in a direction it stays there, this means the plane is natualy less stable but a can be handled faster and wtih more precision.
I work the flight controls systems on the F-15. What you are describing is an aircraft with a perfect rig and pefect cg. This just isn't possible without some type of attitude hold system engaged. You will almost always have some type of movement whether it be in roll, pitch or yaw. That's why we have tolerances for each axis.
A typical checkout prior to doing advanced handling checks will check to see if atleast two of these areas are within tolerance. To check the roll axis they will first maintain a specific altitude, airspeed and check to ensure their wings don't have an excessive fuel imbalance. They will release the stick after placing the aircraft to roll wings level condition and ensuring the aircraft isn't pitching up. They will then start the clock. The airframe is only allowed to roll x amount of degrees per second. Anything outside of this tolerance means the airframe is out of rig. The airframe is allowed to roll some it just depends on whether it's within tolerance or not.
They can also check the rigging on the yaw axis. We call this a rudder friction checkout. So long as the roll axis passed they can proceed to this checkout. The will slowly walk the airfames AOA up. They will reference their check list to ensure they are within a specific set of parameters while doing this check. If the aircraft wants to dump the nose off left or right earlier than it's supposed to then obviously it failed. Just as with the roll axis though there is a tolerance.
The only way to almost guarantee a perfect attitude hold position is to use the attitude hold system itself. If the attitude hold system is engaged rate gyros will be what is used to keep the aircraft at a particular roll or pitch angle. There are limits to this system also (attitude hold can be engaged within x amount of degrees + or - x amount of degrees). The automatic flight controls system comes into play with this area though. It monitors the rate gyros for validity and for current aircraft attitude through the rate gyros. It will hold the aircraft in a particular attitude so long as certain parameters are met. You can temporarily disengage this system by moving the stick to a new attitude so long as you don't go out of the maximum parameters and the aircraft will hold at the last attitude position input.
I know with my stick setup I can point it in a general direction and it will stay like that for awhile. I'll have to go and check it out again sometime. I rarely use it because auto level or auto angle is easier and guaranteed. I'll try to see if I maintain a specific altitude and specific airspeed if I can remove auto level and see if it stays flying at that attitude. The only thing that should keep it from staying straight and level in AH is your stick calibration, steady airspeed and proper cg. As long as your our cg isn't out due to fuel imbalances and your airspeed isn't erratic you should stay fairly straight and level over a period of time after disengaging auto level.
