I think that ID is something of a compromise position between the two extremes. In that, it more or less allows the evidence [or lack of] to speak for itself. It doesn’t insist for the existence of designer, so much as allowing for it.
That is fine theology, but as soon as you allow for a non-natural or supernatural creator (designer, if you will) then you are making a theological, and therefore non-scientific, statement. And ID requires a supernatural or non-natural designer. As theology, I have no quarrel with ID. It's just not science.
In other words, if strict materialism is unable to come up with a plausible scenario for the origin of life, why is not proper to infer that, that the failure of materialism is the triumph [and, de facto evidence] of intelligent design?
Because the absence of evidence is not evidence of absence. Even if the science of abiogenesis never comes up with a plausible scenario for the origin of life (which I find extremely doubtful), it does not mean that there was a supernatural cause. It may simply mean that we didn't look in the right spot or didn't look hard enough where we did look.
Once you bring God into the equation, then science ends:
Why do apples fall? God.
What makes the Earth spin? God.
What causes earthquakes and volcanoes? God.
Why are the galaxies all moving away from us? God.
Why is there only one dimension of time? God.
Why does it appear that the universe is full of dark matter? God.
How does hydrogen and oxygen make water? God.
Where did life come from? God.
This is all fine theology, but it isn't science. And we return to the original question: what should be taught in science class, science or theology?
Also, given that the genetic code shares certain attributes with what we know as information technology, why is impermissible to use the scientific method to explore the possibility that it was, in fact, designed by a higher intelligence?
First, because what you are describing is just that, shared attributes. There are similarities, only because they aim to accomplish similar things, but they are not the same thing. It is, at best, a gross analogy. For example, the formation of crystals in ice also has similar features with the human pursuits of engineering. However, we know that crystal formation has a chemical and molecular basis; we need not posit an "intelligent engineer" to formulate the answer to why they exist, nor is the answer to the question in the realm of engineering.
The second reason is the one I keep coming back to: because allowing the presence of a supernatural creator takes the exercise out of the realm of science and into the realm or religion. Again, if you want to incorporate ID into your religious belief, that it fine. It just doesn't make it science.