Its kind of a tool of necessity isn't it though? The whole point of Godel's second incompleteness theorem was showing a system can never prove its own consistency. You'd need an "outside" system to analyse logic. Since no one has conceived of a way to do that (and on the face of it is impossible and would anyway just result questioning the consistency of that system), you just have to kind of shrug and get on with it, using what we have. Not very satisfying, but here we are.