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The downside of using large stiffnesses is (1) determining how big is big enough to act as fixed, but (2) not too big to cause numerical problems, such as lost digits of accuracy.
The BrIM bridge modeler of SAP2000 V12 uses the stiffness of a cubic meter of concrete, multiplied by about 1e4. This choice is possible because we have some idea as to the size of a typical bent cap or abutment, to which these stiffnesses connect. Thus in kN-m units, AE/L = 1 * 1 * 20e6 / 1 * 1e4 ≈ 1e11. Other stiffnesses such as AG/L, EI/L, EI/L3, etc, are all of about the same order in kN-m units. The value of 1e11 kN/m is used for "rigid" translational stiffnesses, and 1e11 kN-m/rad is used for all "rigid" rotational stiffnesses, converted to the current units.
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