Matrices for rotation have the problem that you are using a 9-dimensional representation for a 3-dimensional quantity, so it is easy to make matrices that are not rotations (indeed the vast majority of the possible space of matrices consists of transformations that are not anywhere close to a pure rotation). Composing matrices leads to rounding errors. It is more complicated to invert matrices. As you say the matrix logarithm is more complicated. Etc.

If you use a scalar + bivector “rotor” representation, that is only a 4-dimensional representation, which is easy to normalize to unit magnitude.