The reason scientists are most interested in a grand unified theory is because theory unification has already had a good track record. It's not because they can't conceive of any other possibility. They just had a pretty good run with theory unification and are hoping it can continue.
They speculatively try all sorts of other stuff all the time, and it mostly doesn't work out at all, so they don't waste too much time on it.
The entire analogy with decimal vs. binary is completely unhelpful. The representation of integers is isomorphic between the two. In particular, 1 is the unit in both because (1, +) generates the entire positive branch of the integers, regardless of whether 1 is written in a decimal representation or binary representation.
I am failing to see anything deeper in your comments than this: "Scientists see this letter: A. And they say, wow, it's a letter, let's study it! But look at this: a. It too is the same letter. Scientists cannot understand this!"
Except of course everyone, scientists included, understand all this perfectly well. I appreciate that you're trying to be thoughtful, but there does not appear to be any substance there.
Scientists are people. They have full access to every way of attempting to understand things that anyone has. Like, if you are studying wrens, and you see a wren with a blue head? You just write that down. No problem. The problem then comes when, despite all that, they still can't figure out what's going on (which is like, all the time--say, they want to know how it is, mechanistically, that male but not female wrens develop blue heads). Then they go, "Okay, fine, we don't understand this. Let's create some falsifiable hypotheses to try to narrow things down."
Because scientists are people, but not for any of the reasons you say, the potential scientific realm is larger than any actualized scientific reach, at least for as long as we have to reach using human brains (and it's not clear whether we can bootstrap our way up arbitrarily far, though computers are giving us a nice extension so far). It has nothing to do with being unable to consider both things and their dual (which I think is what you're getting at with the vase example). Happens all the time. Green's Theorem could be viewed as an example of that.
What you interpret as being unable to access the overall view might be a reflection of two things: first, a desire of scientists to work where it's more tractable, so they explore promising-seeming areas first; and second, experience in how to constrain one's thoughts enough to make progress based on evidence.
It's tempting to think that profound-feeling yet simple thoughts have eluded everyone. Almost always, that's not what's going on--it's usually occurred to a bunch of people and been rejected.
Godel was famous not because he came up with a vague analogical idea. It's because he used a very precise mathematical structure that everyone agreed was really important and was using heavily, and demonstrated that it was impossible to achieve the goal that many mathematicians had as an ultimate endpoint. And it's not about zero at all. It is about a type of self-referentiality.