There is no doubt that choosing the correct blade material to suit your specific print application is very critical. Choose a material that is too soft and you will have to replace it almost every shift, too hard and it may damage your anilox. And if the material is not resistant to the ink or coatings that you are using then it may be chemically attacked and simply corrode.
All that said, if your blade is not rigid enough it will fold over the first time your operator applies too much pressure between the blade and the anilox. Blades that are too thin will also have a tendency to develop a wave in them even with careful installation so will be unable to wipe your anilox evenly across the full face of your roll. This is particularly prevelant in wider web machines. Even when the recommended blade thickness is used many need a back-up material to give it further rigidity and support. If a blade bends to the point that you are no longer wiping with its edge but the back of the blade then you have really lost all control of your wiping action and will potentially cause serious damage to your anilox.
So to some extent blade thickness may initially have it over the material but if you want consistent wiping of your anilox throughout your entire print run you had better make sure you have the right material as well.