The simplifier doesn't recognize that transpose(transpose(x)) is just x.
Neither the verb form $TRANSPOSE nor the noun %TRANSPOSE have any simplifications associated with them.
There's some tension between applying transpose or any operator in simplification and leaving some operations to be carried out in evaluation (e.g., should 'transpose(matrix(...)) simplify to the actual matrix, transposed? I dunno). But I'm pretty sure transpose(transpose(x)) should be simplified.