In the 50 years I have been in our hobby, I have not seen or heard of any reports of brake failures brought about by woven or bonded lining materials, or by riveted and bonded applications.
Cast iron on woven brake lining has a static coefficient of friction = 0.35 to 0.40, and
steel on woven brake lining has a static coefficient of friction = 0.22. Cast iron also has a better heat transfer coefficient than steel. Considering the coefficients, woven brake lining is better with cast iron than it is with steel, and overall cast iron is a better brake drum material. This explains one reason why automakers went away from pressed steel brake drums in the 1930s. Clearly, the ease of manufacturing cast iron drums is a cost advantage over pressed steel drums.
From about the 1860s to the 1930s, woven brake lining ruled the market place because it was producible by the weaving manufacturing technology of the time period. However, as more modern chemistry came along in the late 1930s, molded linings became less expensive to manufacture.
Asbestos found its way into woven linings and early molded linings which would bring about their eventual demise. However modern chemistry adapted space age ablative materials into molded linings, so they have survived.
Brake technology as a whole was driven by the aviation industry that had to cope with heavier aircraft and higher landing speeds. Imagine the brakes it took to stop a WW2 era B29 Bomber!