The trim required to keep the aircraft flying straight and level is too great (high)
A table is provided in the 737-600~900 Fault Isolation Manual for various configurations, speeds and altitudes. e.g. cruise (flaps up/Gear up) at .78 mach at 37,000' or more, aileron trim limit is 0.75units and rudder trim limit is 0.5 units. Consideration must be given to fuel load and thrust balance.
If the flight crews don't have access to this table (except on the test flight), it seems a pointless exercise
Rgds
NSEU