Saying we consider time reversibility true for more or less philosophical reasons seems a bit of an understatement to me. Conserved quantities prevent states differing in at least one conserved quantity from ever evolving into the same state, i.e. conserved quantities partition the phase space and states cannot cross those partition boundaries. This also has to hold for all isolated subsystems. And conserved quantities arise from symmetries like homogeneity and isotropy of space which are pretty solid empirical and experimental facts. It's all interlinked and I imagine it would not be to easy to eliminate time reversibility from the laws of physics without causing some odd consequences.