Consciousness and other brain states are not properties of you, the 4-D entity. They are properties of particular time slices of that 4-D entity, and different time slices can instantiate different properties. So it is a category error to ask "Why don't I have consciousness of all times?" if by "I" you're referring to a 4-D entity and not an individual time slice. 4-D entities are not the sorts of things that are conscious. Time-slices of (certain) 4-D entities are. I don't even know how to answer your final question, because I have no idea what you mean by "4-D consciousness".
Now maybe we can re-word your question like so: "If all times co-exist, why don't my time-slices have consciousness of all of them?" But the answer to this question is simple: Your time-slices do have consciousness of all of them (at least, all of the ones between your birth and death). It's just that different time-slices are conscious of different times; each one is conscious of the time at which it is located. It is (currently) true that my time-slice from two hours ago (who is located at a time two hours in the past of the time I'm typing this) is conscious of that time.
An analogy: Suppose you invent a time machine. You use the time machine to travel three years into the past. As a consequence, there are now two spatially separated "yous" located at the same time -- the "you" from three years ago and the "you" who just time-traveled. Let's say the former is in England and the latter is in Greece. Surely you wouldn't expect each one of the "yous" to have some sort of combination of England and Greece experiences. You'd expect the one in England to have England experiences and the one in Greece to have Greece experiences. For similar reasons, the eternalist should expect each time-slice to have experiences specific to its own (space-time) location, not some combination of the experiences of all time-slices. And, indeed, that is what we observe. So I don't think there's any deep mystery here.
To explain the phenomenology of passingness, then, reduces to a problem of explaining why each time slice identifies strongly with other time slices, and the particular structure of that identification. The way in which my current time-slice's psychological states are related to those of past time-slices is very different from the way in which they are related to those of future time-slices. Also, the way they are related to proximal past time-slices is different from the way in which they are related to those of distal time-slices. I think it is analyzing the nuances of these cross-temporal relationships that will get us farthest towards understanding the phenomenology of temporal passage (at least, as far as we can get without a solution to the hard problem of consciousness). A-theory and presentism, by contrast, do not help me understand passage at all, so I really don't see their advantage in this regard.
...Consciousness and other brain states are not properties of you, the 4-D entity. They are properties of particular time slices of that 4-D entity, and different time slices can instantiate different properties. So it is a category error to ask "Why don't I have consciousness of all times?" if by "I" you're referring to a 4-D entity and not an individual time slice. 4-D entities are not the sorts of things that are conscious. Time-slices of (certain) 4-D entities are. I don't even know how to answer your final question, because I have no
I've always been puzzled by why so many people have such strong intuitions about whether the A-theory or the B-theory1 of time is true. [ETA: I've written "A-theory" and "B-theory" as code for "presentism" and "eternalism", but see the first footnote.] It seems like nothing psychologically important turns on this question. And yet, people often have a very strong intuition supporting one theory over the other. Moreover, this intuition seems to be remarkably primitive. That is, whichever theory you prefer, you probably felt an immediate affinity for that conception of time as soon as you started thinking about time at all. The intuition that time is A-theoretic or B-theoretic seems pre-philosophical, whichever intuition you have. This intuition will then shape your subsequent theoretical speculations about time, rather than vice-verse.
Consider, by way of contrast, intuitions about God. People often have a strong pre-theoretical intuition about whether God exists. But it is easy to imagine how someone could form a strong emotional attachment to the existence of God early in life. Can emotional significance explain why people have deeply felt intuitions about time? It seems like the nature of time should be emotionally neutral2.
Now, strong intuitions about emotionally neutral topics aren't so uncommon. For example, we have strong intuitions about how addition behaves for large integers. But usually, it seems, such intuitions are nearly unanimous and can be attributed to our common biological or cultural heritage. Strong disagreeing intuitions about neutral topics seem rarer.
Speaking for myself, the B-theory has always seemed just obviously true. I can't really make coherent sense out of the A-theory. If I had never encountered the A-theory, the idea that time might work like that would not have occurred to me. Nonetheless, at the risk of being rude, I am going to speculate about how A-theorists got that way. (B-theorists, of course, just follow the evidence ;).)
I wonder if the real psycho-philosophical root of the A-theory is the following. If you feel strongly committed to the A-theory, maybe you are being pushed into that position by two conflicting intuitions about your own personal identity.
Intuition 1: On the one hand, you have a notion of personal identity according to which you are just whatever is accessible to your self-awareness right now, plus maybe whatever metaphysical "supporting machinery" allows you to have this kind of self-awareness.
Intuition 2: On the other hand, you feel that you must identify yourself, in some sense, with you-tomorrow. Otherwise, you can give no "rational" account of the particular way in which you care about and feel responsible for this particular tomorrow-person, as opposed to Brittany-Spears-tomorrow, say.
But now you have a problem. It seems that if you take this second intuition seriously, then the first intuition implies that the experiences of you-tomorrow should be accessible to you-now. Obviously, this is not the case. You-tomorrow will have some particular contents of self-awareness, but those contents aren't accessible to you-now. Indeed, entirely different contents completely fill your awareness now — contents which will not be accessible in this direct and immediate way to you-tomorrow.
So, to hold onto both intuitions, you must somehow block the inference made in the previous paragraph. One way to do this is to go through the following sequence:
One potential problem with this psychological explanation is that it doesn't explain the significance of "becoming". Some A-theorists report that a particular basic experience of "becoming" is the immediate reason for their attachment to the A-theory. But the story above doesn't really have anything to do with "becoming", at least not obviously. (This is because I can't make heads or tails of "becoming".)
Second, intuitions about time, even in their primitive pre-reflective state, are intuitions about everything in time. Yet the story above is exclusively about oneself in time. It seems that it would require something more to pass from intuitions about oneself in time to intuitions about how the entire universe is in time.
1 [ETA: In this post, I use the words "A-theory" and "B-theory" as a sloppy shorthand for "presentism" and "eternalism", respectively. The point is that these are theories of ontology ("Does the future exist?"), and not just theories about how we should talk about time. This shouldn't seem like merely a semantic or vacuous dispute unless, as in certain caricatures of logical positivism, you think that the question of whether X exists is always just the question of whether X can be directly experienced.]
2 Some people do seem to be attached to the A-theory because they think that the B-theory takes away their free will by implying that what they will choose is already the case right now. This might explain the emotional significance of the A-theory of time for some people. But many A-theorists are happy to grant, say, that God already knows what they will do. I'm trying to understand those A-theorists who aren't bothered by the implications of the B-theory for free will.