You employ the qualifier of "if" in order to perhaps indicate that this is just a hypothetical so I will also use that qualifier.
For the "comfort" of mixed company, I used "if."
If the being in question is omnipotent, then he wouldn't have to exist everywhere at once to know what is happening in his universe. Better yet, why would someone who could avoid such an experience which involves personally being present in every single latrine, sewer, fecal-filled intestine, sperm engorged gonad, festering sinful mind, decaying cadaver, refuse filled garbage bin, cancerous pus oozing ulcers, and having to personally witness rapes, child abuse, murders, mutilations, bestiality, all types of sexual abnormalities that he tags as abominable force himself into those places in order to know that it is going on when he could easily avoid it?
Omnipotence is not omniprence by definition. Omnipotence is the absolute power to do absolutely anything.
Omniscience is a consequence of omnipotence.
BTW
There are also certain assumptions or premises on which your conclusions are based that I find baffling.
For example, why would an omnipresent being be unable to exist without omnipotence and why would he be unable to be omnipotent without being omnipresent? In short, why would omniscience force any omnipotent being to be omnipresent when he could easily know all things at a distance without it?
It isn't about forcing anything; omnipresence is a consequence of omniscience. As exained above, if you are omnipresent, you exist everywhere - every dimension, time, and point in all of creation ever.
If we choose a time interval dt to represent infinite infinitesimal length of time, then each moment is a sum of infiniteesimal sums. In order to get to infinitesimal, you have to be able to "count" to infinity - which requires an infinite lifetime + the time not included before a count was started. This omnipresence - to be nontrivial - is defined by the power to be at that infinitesimal interval for an infinite time, scaling the time to normalization. So,
you must be able to exist u til the infinity count is over before you can assuredly say you are absolutely omnipresent. Or, you need to be infinity itself plus some constants not included in the count.
That is the consequence from omnipotence - that you
can quantatatively exist in an infinitesimal time interval for an infinite amount of time. And, this is over all dimensions in all creation. Anything less, and you are not omnipresent.
You cant omnipotent at a distance, because being omnipotent categorically means you have all power - including the power to exist everywhere. If you are not exuding all power, you are not OMNIpotent. If you are omnipotent at certain time intervals, the you aren't omnipotent fully. Omnipotence requires omnipotence at normalized scale - all power over infinitesimal intervals of space and time, for infinite duration over the entirety of creation.
Omnipresence
follows from being all powerful.
And, omnipotence follows from omniscience.
After all, if knowing things at a distance is beyond his ability then he would not be omnipotent. Curiously humans are easily able can know things at a distance and even accomplish many things at a distance So imagining God incapable of it on a universal scale seems quaint.
It is a paradox: omnipresence does not exist without omnipotence, because it is a consequence of omnipotence. But now you are talking about science - knowing things at a distance. That isn't omniscience; it is simply science.
And, science does not produce infinite potency - unless your knowledge is infinite also.
This is why: if you are omniscient, you are omnipotent, and if you are omnipotent, you are omnipresent. They are consequences, respectively. You cannot be omniscient, for example, and not have the knowledge to be omnipresent. You cannot be omnipotent, and not have the ability to exist everywhere. They are tripled characteristics.
Also, there is no compelling logical reason why mindlessness cannot be eternally self-perpetuating.
In these cases, logic reaches an asymptotic limit when dealing with infinites. If you are
mindlessly omnipresent, as you suggested, then you are implying someone was able to be innumerable present everywhere - all of the time -
with limited, or retarded knowledge. That isn't possible in the paradox; omniscience (implies omnipotence, which) implies omnipresence.
As I said before, in order to truly be OMNI anything, you would need to first be able to reach infinite normalization (an infinity over infinitesimal intervals.) So, you at least need omnipotence to have the power to get to infinity in "count." You need omniscience to know how to count to infinities. So, when dealing with OMNI anything, these characteristics are at the base a demand in coupling omniscience and omnipotence.
Please keep in mind that mindlessness demand a total inability to think, perceive things in a logical way, recognize patterns and draw conclusions, and therefore act on those conclusions to accomplish a goal.
Then, you aren't omniscient. And, if you are not omniscient, you don't have the knowledge capacity to do anything (omnipotence.) And, if you are not omnipotent, you don't have the power to be everywhere (omnipresence.)
Again, they are tripled.
Mindlessness is a retardation, or dampening of science.
The only way to sever or interrupt such a self-perpetuating mindless sequence is to violate the conditions of the hypothetical and introduce some semblance of self awareness. Unfortunately doing so violates the conditions of the hypothetical which is the condition of mindlessness itself.
Which is why you can't be omniscient if you are mindless - which means you aren't all powerful, and thus you do not have the power (or intelligence) to be everywhere all the time at any time in any space for any dimension. If you lack one thing (like self awareness, for example,) you cannot define yourself as an omni.
The paradoxical characteristics are tripled.
This is similar to the violating the hypothetical of attempting square a circle. As long as we abide by a circle's dimensional parameters, of course, it remains a total impossibility t5o square it mathematically. However, if we change those dimensional parameters then the circle ceases to exist as a circle and squaring the resultant figure doesn't count.
You can square a circle without being omniscient. You can't be omnipresent and be mindless at the same time. For one thing, you would need an *extra* omniscient/omnipotent/omnipresent entity to
verify one's mindless positioning - since the one who is mindless will it be able to verify for itself if it is everywhere all of the time...
That necessary *extra* "Omni" is the
actual omnipotent/omniscient/omnipresent entity. It is not the mindless one who lacks omniscience and omnipresence, and can only confirm it's omnipresence by an outside entity.
The characteristics are tripled.
BTW
A certain religious denomination considers God omnipotent but not omnipresent. From its perspective God knows what is going on in his universe without being personally everywhere just as humans can know what is going on at long distances without being personally at the locations.
That fails. You cannot know every single thing about every single position at every single time in every single dimension for every single creation if you are not at those places all of the time. If God is omnipotent, then He has the power to do everything - including be everywhere all the time, at the same time, for every dimension, in every infinitesimal time interval, over infinite quantification of parameters.
Categorically, God would get his omnipotence from His omniscience - which would also allow Him to categorically b3 omnipresent.
Now, if we are talking about God phikisophicalky "choosing NOT to be everywhere" at the same time... then that is an exercise in the mind of an omnipotent/omniscient entity - a different story than setting the parameters of what MUST and MUSTN'T be possible for an omnipotent/omnipresent/omnipotent entity.