Why does writing seem dependent on agriculture and states?
I think you're overstating the frequency with which writing systems have been created. You could alternatively be asking "Why did so few agricultural societies not invent writing?"
There is another personality of course which is that the invention of writing simply occurred late enough in the timeline of the past that it coinciding with non-hunter-gatherer societies is exactly that: A coincidence.
Lets look at these two possibilities.
Think of all the writing systems you can. Let's ignore things with a recent history of creation like Hangeul (15th century) which is unquestionably based on earlier systems, and things like Cree syllabics, which were developed as a replacement for other/earlier writing systems (in other words, they weren't created by non-literate societies).
Looking just at older writing systems, how many can you come up with? For the sake of brevity lets say that the diversity can more or less be represented by selecting Cyrillic, Greek, Arabic, Hebrew, Latin (and thus English, obviously), Devanāgarī, Tibetan, Chinese, Cuneiform, Aztec/Nahuatl, and finally Egyptian hieroglyphs.
Of those, we can say that obviously Aztec, Cuneiform, Chinese and Greek are unrelated. They were developed without likely contact between any of the groups using such systems.
But actually, of the rest, they really can be linked back to a single system in the distant past.
You see the pattern.
Korean is stylistically heavily influenced by Chinese brush script, but also has been argued to take features from 'Phags-pa. 'Phags-pa of course being based on Tibetan, which again gets us back to Phonecian.
But sure otherwise we can say Chinese is a separate thing from these Phonecian scripts. Same for Cuneiform and Aztec writing. But how many people do you know that are using Aztec-derived scripts? I can't think of any.
So perhaps a better question is Why are so many groups using Phoenician-derived scripts?
The obvious answer is that they're useful and so were adopted.
The point, though, that I'm trying to make is that you should not underestimate just how rare the genesis of truly new scripts actually is. It almost never happens, and in the entire history of man, it has only happened a handful of times. What's much more common is gradual changes in those script which cause them to become separate entities. Slightly less common but still happening, especially these days, is the creation of new scripts which are conceptually based on the existing scripts but without the same sort of history of development and depth that we see for things like early Egyptian and Chinese writing. Rather, today's version looks much more like the Cree example I said to disregard at the beginning.
So really, relative to the world's number of historical languages, the occurrence of the invention of writing is basically a statistically anomaly. It nearly never happens. As for why you're not seeing it in hunter gatherer societies, there is of course the question of need (as in, of what use would it be, especially given the importance of oral tradition), but even ignoring that, the more significant reason is because writing is historically almost never invented.
And of course there's the point that perhaps hunter-gatherer societies did invent writing, but not on a medium which has survived to the present. Writing on animal skins in the jungle isn't going to last as long as baked clay tablets have.
As a side note, you may also be interested in this question from a couple weeks ago.
tl;dr: Because historically, almost no one has invented writing.