There is no evidence that adopting personal routines leads to cognitive decline in the way that you have described in your post. There is some evidence that a propensity against personal routine can be representative of underlying creative potential. Given that creativity is highly linked to openness to experience on the Big 5 measure of personality, this could be representative of higher intelligence in certain contexts. However, this does not implicate that personal routines decrease one's existing cognitive capacity.
LONG, DETAILED ANSWER:
In your first paragraph, you refer to these daily routine tasks as 'automated', in the sense that they 'spare... mental energies for [other] tasks'.
In your second paragraph, you wonder if said tasks could contribute to a decline in cognitive processing, given that you are (presumably) doing many of them over a long period of time.
For this reason, I think that a computer is not a perfect analogy. A computer may do things 'automatically' (as in, they are pre-programmed to do so). However, the computer still 'runs' this program as it would any higher-level algorithm. The automatic routine may take up less 'space', but I believe it still requires its own subroutine or threaded code (pardon me if my terminology is incorrect, I haven't quite learned how computer systems work yet), thus 'wearing down' the computer over time.
A human performing a daily routine is not the same as a computer performing a recursively-called subroutine. A human performing a routine is engaging in an unconscious and regularly-repeating habit. Because these habits are unconscious, they do not contribute to cognitive decline in the way that you are referring to. Certain routines may be harmful for other reasons (e.g. routine shopping trips without knowledge of money management, routines that aid procrastination, etc.), but in many ways, routines can actually reduce cognitive load, thus freeing up the mind to focus on other things.
The downside is that they take longer to implement, unlike an algorithm. Lally et. al (2009) found that habits take anywhere from 18-254 days to become asymptotically 'automatic', with an average of 66 days. They are also harder to eliminate if they turn out to be harmful. This is augmented by the fact that the basal ganglia remembers the 'triggers' that helped initialize the routine in the first place, and thus routines can be revived if the triggers reappear. (As this article from MIT points out, "Old habits don't die. They hibernate.").
From the third paragraph in your question:
On the other hand, I can also see how personal routines and daily automation are an earmark of highly intelligent people who are capable of seeing patterns between two separate instances of a similar task. But can a side effect (automation) of that initial favorable cognitive state (IQ) lead to lowered cognition as a matter of lessened daily mental workout? In other words, can you become dull if you do things more routinely?
I don't think that daily automation and personal routines are necessarily the 'earmark of highly intelligent people...' in the way you are describing. Given that automatic routines are unconscious activities, they are marked by a lack of cognitive processing, no?
However, the ability to develop and stick to a pre-planned routine to the point that it becomes automatic does depend, to some extent, on specific areas of the brain that help regulate executive functioning. I already mentioned the basal ganglia, but the prefrontal cortex (and other areas of the frontal lobe) have been implicated in planning complex cognitive behavior, as well as decision making. These areas are further responsible for task switching, as well as cognitive inhibition of unnecessary impulses and short-term gratification.
IQ itself is not necessarily a matter of activity in the prefrontal cortical regions. You can have a high IQ and have decreased dopamenigernic activity in the mesolimbic reward pathway, thus making it more difficult to automate desired behaviors. You may also find yourself struggling with complex cognitive planning if you have decreased network connections in your prefrontal cortex. However, your intelligence quotient depends on a variety of other neuroanatomical factors besides chemical activity in these regions. The size and shape of the frontal lobes, the amount of blood in the frontal lobes, the total amount of gray matter in the brain, the overall thickness of the cortex, and the glucose metabolic rate all seem to affect IQ.
In terms of making oneself cognitively 'dull' by use of routine, I wouldn't necessarily go that far; however, it is worth mentioning a phenomenon called latent inhibition, which is a personality trait in humans (some more or less than others) in which routine or familiar events become hardly noticeable. Those with low latent inhibition may perceive stimuli as if it were brand new (like a child seeing the world for the first time). From the section on low latent inhibition (courtesy of Wikipedia):
Most people are able to ignore the constant stream of incoming stimuli, but this capability is reduced in those with low latent inhibition. Low latent inhibition (that may resemble hyper-activity or ADHD in early decades of the individual life) seems to often not correlate with distracted behaviors. This distractedness can manifest itself as general inattentiveness, a tendency to switch subjects without warning in conversation, and other absentminded habits. This is not to say that all distractedness can be explained by low latent inhibition, nor does it necessarily follow that people with low LI will have a hard time paying attention. It does mean, however, that the higher quantity of incoming information requires a mind capable of handling it. Those of above average intelligence are thought to be capable of processing this stream effectively, enabling their creativity and increasing their awareness of their surroundings. Those with average and, less than average intelligence, on the other hand, are less able to cope and as a result are more likely to suffer from mental illness and sensory overload. It is hypothesized that a low level of latent inhibition can cause either psychosis or a high level of creative achievement or both, which is usually dependent on the individual's intelligence. When they cannot develop the creative ideas, they become frustrated and/or depressive.
So, in short, a natural propensity against personal routine may (or may not) be a sign of underlying creative potential, as low latent inhibition may make it naturally difficult to develop and stick with routines to the point of automaticity. However, like many things, this requires context and is not a blanket statement that can generalize people at large.