It's a very broad inspiration and the ones who most closely hewed to biological systems were some of the least successful - most flying machines don't use active wings with highly variable geometry. The first successful human flying machines didn't have a meaningful biological equivalent at all.
Depending on your perspective, the airplane is not successful until we figure out how to do it sustainably. We may yet have to go back to lighter than air flight, which arguably has precedent if you count aquatic life, i.e. swim bladders.
Unless we start making the sustainability of our technology a success criteria, we'll never achieve it. Many biological systems are different precisely because they are constrained to run within an overall sustainable system.
Maybe human tech ~is cyclically sustainable on a long enough timescale, but I certainly ~hope we're not going mostly to die off and live without technology until the forests grow back and microorganisms in the oceans turn into oil.
Sustainability is not something optimized by natural selection either, all that matters to get a trait adopted by a population is that it provides a reproductive advantage to the individuals with the trait, which has frequently in the past resulted in ecological collapse. The most disastrous and classic example being the first organisms to emit oxygen which at the time was a deadly poison, is assumed to have killed a huge percentage of the species on earth, and could easily have resulted in a genuine full wipe.
We're smart enough that we should be able to avoid anything like that if we put in the work but don't glorify what's natural, we should be looking for our own solutions.
The three-axis control system (in particular the concept of ailerons) developed by the Wright Brothers was inspired by the way birds twist their wings.
The process being that the people who took inspiration from animals died out and gave way to the people who were better able to adapt to changes in modern technology like the propeller and internal combustion engines?
