You are very much overestimating how much attention people pay to the faces in a crisis, even without accounting for the fact that Mathilde can change her face - so our enemies both have less reason to look into it and if Mathilde thinks it's going to be relevant for some reason, she can simply look like the rider instead.Why though? It's just like the Mathilde option but significantly less useful in some of the scenarios we'd want to use it in.
Bodyguards chasing an assassin or guards chasing a thief are likely to look at the face of the prison they're fighting to see if they're the one they're looking for.