Use pivoting as the default in LU regardless of the element type. (#32989)
For types that weren't subtypes of AbstractFloat, we used to try
to LU factorize without pivoting and only use pivoting when it failed.
This caused large numerical errors when computing the LU for element
types which promoted to float like numbers such as most integers.
The behavior was never documented and is error prone. Hence, this
PR removes the behavior.