Structures in living systems often came about by such a process. Features that had made intermediate forms adaptively useful are not in evidence, but sometimes appear in related species, or in embryonic development. Evolution cannot plan for the future, but it is happy to discard what is not useful anymore. It is our challenge to imagine the structures discarded, and how they were useful in that form, and scientists' to find evidence preferring one path of development over others.

Anyone can give up and say "God did it" on any day. Others do not give up, and biology as it stands today is a product of not giving up. We might wonder how it could have got here, but it too has come through many intermediate forms, with much since discarded.

Also the identical solutions that appear in different species are named "convergent evolution" (e.g. the eye of vertebrates and cephalopods); it is by no way a validation of gradual evolution because chance could not build the exact same solutions. It is on the contrary a proof of design (reuse of building blocks)

"Irreducible complexity" is specifically what the arch principle answers. The uncompleted arch along with everything holding it up is of immediate value, as it is, for maximizing reproductive fitness; it is our task to understand how. Later, the completed arch has value as, possibly, something entirely else, where the scaffolding did not and fell away.

Nature doesn't care what the arch or its intermediate forms were "for". Any structure may be used in any way that aids fitness (or, often, not). Insects' extra wings become protective wing covers. Legs that were once fins may walk instead of swimming, or fly, or type. T. rex's arms, and ostrich's, waggle uselessly.

The evolution of eyes has been traced from eye spots through to completed eyes, and each intermediate stage is in fact better for reproductive fitness than the previous one. The form of eyes is dictated by their use, but human eyes' present form is decidedly inferior to squids'. (Ask your God about that?) It has lately turned out that the basis for eyes was already in the last common ancestor of squids and us. It has been a very long time since eyes were a persuasive example. Maybe read up?

About the eye, which common ancestor to squids and vertebrates is it ?

You are aware that all species that existed 500 million years ago are extinct, leaving only their descendants? That would include our common ancestor, leaving squids, and us, and fruit flies. (Some coeval species left fossils, though probably not that one.) But the gene that places our eyes, inserted into a fruit fly chromosome at a place dictating growth of a body part, grows an eye there. A fruit fly eye, of course.

Careful: claiming software you wrote is divinely inspired will not go over well at code review, particularly if you insist it doesn't need to pass tests.

So, a series of not-excessively-harmful monkey-patches accumulate under stringent testing to significant improvement. We don't need to guess about that: it has been demonstrated by laboratory experiment, which you may read all about if you care to. Or don't, and continue parroting Behe's sterile talking points long after they have been thoroughly discredited.

It is not 'pure logic' because your analogy is flawed - biological systems are not arches or mousetraps. Imagine a system as a triangle of three components that all rely on each other. The vertices of the triangle are component (proteins, organs, whatever) and the edges are 'dependencies' of some kind.

Now add a fourth component, dependent on some (or all) of the others. Now remove some of the edges until you have a square (or 4-cycle). Now this system is 'irreducible' as breaking the dependent links breaks the cycle.

Essentially, all biological systems have a 'chain' of previous versions that were functional and evolvable into the next version. This is only possible because these systems have redundant parts, and flexible associations. For example, many proteins 'moonlight' as alternate roles within an organism.

"Since biochemistry darwinists have to work and to prove now!" - This sentence doesn't even make sense. It is Intelligent Design advocates like Behe that are making the claim that these systems "could not" have evolved.

As another commenter said, this is the 'Argument from Ignorance' : "We do not know how it evolved so it could not have!". We know the structure of biological systems in more and more detail. We know how they change at the smallest level. The theory is fairly basic : redundant, self-assembling, flexible systems can change through gradual evolution.

Gould would talk about 'rewinding' the tape of history. There's no way to go back in time and see for sure what previous systems looked like. However that in no way means the tape itself does not exist.

Nature has no problem building an arch through a long series of small changes, no keystone required.

Changing a single bit in computer code is very likely to have an arbitrarily large, commonly fatal effect. Changing a single base in a gene rarely does. But a lot of bases changed is likely to have some effect; the more changes, the more effect.

What critics of natural selection always miss is that the set of small changes between one state and another, in a breeding population, do not need to happen one after the other. It could take hundreds of steps, but they all may exist scattered through the population at the same time, and can over just a few dozen generations propagate to all, when conditions favor that; or even fewer if lacking most is fatal.

Bacteria need a lot more generations to evolve, because they don't swap genes around much. But their generations are very short. Some mutations they do swap around, particularly antibiotic resistance, and ability to infect a new host, via plasmids. Anthrax normally lives in soil, but picks up virulence genes from plasmids it happens upon.

The creative power of randomly mutated code is, again, easily verified.

These are two different things though, separated by maybe as much as one billion years.