And it is also structured hierarchically- I agree it doesn't always increase complexity: in fact degradation I would argue is more directly apparent: we see clear examples of birds losing flight, fish losing sight, and I think we both agree on how this occurs: Entropy- in the sense of decay, chaos
Losing features that are no longer advantageous is an adaptive evolutionary change. When there's no longer a selection pressure for maintaining them, detrimental mutations will erode their function - but such features are also disadvantageous, an unnecessary drain resources that could be better used on more adaptive traits, so there is a selection pressure against them. When you consider marine mammals, from pinnipeds to cetaceans, you can see how the loss or modification of limbs has resulted in more adaptive traits.
How these are gained is a far more difficult question, and somehow we got from a single celled bacteria to the entire biosphere as we know it, so we can't really avoid the fact that vast new volumes of functional information has to be provided along the way somehow.
It's not the problem you think it is - in extant life we have examples of every major stage of evolution necessary for that 3.5 billion year journey. From the first stages of multicellular cooperation in bacterial quorum-sensing, producing films & mats, through sponges and Cnidaria (jellies, jellyfish, etc), right up to vertebrates, insects, etc.
Fighting upstream against entropy with blind chance (random mutation)... is just supplying more entropy into the mix, accelerating your decent downstream
It's true that by increasing complexity, you accelerate the increase in entropy, but it's not the problem you think. When entropy gradients are at their steepest, e.g. shortly after the big bang, the energy flows are too energetic for complexity to appear - as the gradients begin to reduce, atoms can form, then molecules, and eventually it's calm enough for them to begin to clump together into dust clouds and form stars and planets.
Stars are low-entropy energy concentrations that, in increasing the entropy of their surroundings provide a steady stream of energy to them. Planets receive this steady stream of low entropy energy and dissipate it as heat, increasing the entropy of their surroundings. This 'free energy' supply drives chemical reactions in gas clouds, on asteroids, and on planets, that dissipate energy even more effectively. On planets with suitable conditions, this free energy will drive reactions of increasing complexity, which dissipate energy and increase the entropy of their surroundings even more effectively.
So it is a medium entropy gradient, as found in our current epoch of the universe, when the free energy can drive the development of complexity. As the overall entropy increases and the energy sources begin to expire, there is not sufficient free energy to maintain complexity against the increase in entropy. As thermodynamic equilibrium approaches, free energy has been dissipated, and complexity is unsustainable.
A simple analogy is in the flow of water; where the gradient is very high, e.g. a waterfall, the flow is so turbulent that no organisation or complexity can develop or persist. when the flow is fast but not turbulent, eddies and whirlpools can form, taking enough energy from the flow to produce movement courter to the direction of flow, and maintaining themselves using the steady force of the flow. When the flow becomes very slow or ceases, the eddies and vortices reduce and eventually die out, there is not enough energy in the flow to sustain them.
It's true that without the development of complex structures entropy would increase more slowly, but the action is towards maximising the increase in overall entropy - developing and maintaining complexity does this most efficiently (e.g. forest fires and global warming!).