So what happens if we unplug the computer? Isn’t that a halting state??
There seem to be several unstated assumptions at work here.
First, MI is not a thing that exists in a physical way, it is a measurement between two systems (say A and *B). If A and *B are identical or nearly identical then they will share a high degree of MI. We can easily imagine a physical process that produces identical copies of the same system; for instance, all water molecules share a relatively high degree of MI. By this argument all water molecules (and all matter!) is designed.
It is more interesting to consider some system A than is capable of making copies of itself, creating a child system B that can also make copies of itself. Here the MI should contain the information relative to the_function_ of reproduction. Again, we can name physical processes that reproduce themselves, such as fire. Fire possesses some of the qualities of life; it metabolizes fuel from the environment, and can spawn other fires nearby via sparks. On state of “on fire” is very similar to any other state of fire, so they should have MI between them. Is fire designed? I think not.
So far we have at least two examples of MI that do not require intelligence, unless we want to declare everything to be designed, which is not useful in a scientific sense.
We can continue this exercise by adding functions in addition to replication. For instance, can the process capture energy from the environment? If we count hot embers as stored energy, then fire again appears to be designed. Capturing energy is also implied in the function of reproduction.
But what about capturing information from the environment? Now we have something different. Fire clearly doesn’t have any “memory” about what it burned before. Fire never gets any better or worse at burning, it just continues to burn until it exhausts itself. I claim that capturing information from the environment is a key function for sometime to be “life”. Capturing information separate life from other chemical processes that we would not claim to be alive. There could be additional functions needed depending on how we define life, but reproduction and capturing information are essential.
[edit:: clarifying: Where and when halting occurs is another hidden assumption, or at least undefined]
Considered as an algorithm, a system A that reproduces itself is a forking process. The forks produce child systems B and C (with slight variation) which continue. If C is better at reproducing itself than B we will get more copies of C in the environment than B. If B and the children of B are effectively unable to reproduce, then the B process halts. The remaining process C has gained*** information relative to successful reproduction (fitness) from the environment.
*** clarification: C has not lost information relative to fitness, and may have gained relative to A.
Once such a system as A and C exist in the environment there is no barrier to adding additional information other than the environment itself. @EricMH may still have a case for the initial MI, but the idea needs further refinement to avoid the “everything is designed” implication.