Maybe it'll continue making a cultural impact as more and more movies are produced. But I don't see kids wearing clothes, playing with toys, or eating food with Avatar slapped all over it.
I mean, that's down to a marketing approach, rather than anything else.
By your logic here, films like all the terrible "Trolls" animated movies have huge cultural impact, because their marketing is entirely directed towards kids and branding for kids. Indeed, all sorts of terrible and immediately-forgotten movies are kind of a big hit with kids, or if not a hit with them, then marketed to them so aggressively that you see them eating their [terrible movie] Happy Meals and so on.
Avatar has done a lot of marketing, but none of it has been child-focused - the focus instead seems to be to market it as a spectacle and a family film.
It feels like the logic here is "Unless it plays out exactly like Star Wars, it has zero cultural impact", which is a pretty weird take, albeit a common one.
I think the other issue that people aren't really processing is that Avatar 1 was a single movie 14 years ago. So expecting it to have a big impact is pretty bizarre. If The Matrix had ended at The Matrix, I think it'd be almost entirely forgotten, for example (as Sky-Captain is, for example, only the nerdiest nerds remember that). There's also a weird double-standard that's applied here, where no-one questions, say, the Bay-era Transformers movies having left essentially no trace on pop-culture apart from Youtube videos about how demented they are. It's like, what exactly are people expecting from a single film? I guess Terminator-style kiss-off lines is the answer, but the original very much wasn't that kind of movie.
The second one, which is a less trope-y and predictable movie still eschews kiss-off lines and the like, but it does have rather more engaging plot, even if it has some overlong sections in the middle. The action finale is on-par with anything Cameron has done. I think the real assessment as to how much impact the series has had won't be able to be made until it's over. I will say that I think the reason a lot of people liked to talk about cultural impact was that they thought it was over - that there never would be a sequel - or were trying to wish that into being the case.
There's also a complicated cultural issue going on with these movies which could take paragraphs or even pages to discuss, but which essentially boils down to:
1) A lot of educated and influential people are extremely uncomfortable with Americas-style colonialism being critiqued. These same people may be fine with critiques of colonialism and imperialism as it manifested in say, the British Raj, or Colonial Africa, but they're uncomfortable with critiques of Americas/Oceania-style stuff.
Keeping this short, I think this is very evident in a lot of the negativity shown toward the movies by certain people, and similar negativity they show towards any movie that attempts to critique colonialism/imperialism in the US - you saw this with Dances With Wolves, for example - hugely popular, hugely successful, critically fairly well-received, but a lot of people at the time and later tried to find ways to say it should be ignored or dismissed - and it's curious how that happens to literally any movie which attempts to critique that particular type of colonialism.
This is really a super-complicated issue that I think people could write entire papers on, but I think it's a real one.
1a) Worse than that, I think there's a weird line of vague but intense racism present again across the political spectrum which essentially works out as "tribal-style indigenous cultures aren't
real cultures, only ones which had highly developed and obvious civilizations are". No-one will ever say this, but it's curious how many well-educated people will happily rant about how awful the British Empire was in India (and it was!), yet basically shrug at the utter horrors inflicted on the Native Americans, or even essentially suggest "they had it coming".
2) Awful nerds can't stand it when the guys with the cool tech and macho lines aren't the good guys.
This is just a hard fact. Some nerds are awful and lot of them get intensely uncomfortable if they guys with the coolest tech aren't also the good guys. This even hits Star Wars, creating the weird people who clearly love everything about the Empire despite knowing they're the baddies. And the baddies in Avatar do have all the cool tech. I do think Cameron missed a trick a bit by not giving the animals more personality/intelligence - minor spoilers for Avatar 2 -
the one who he does, the extremely agile whale-thing, is one of the most memorable characters in the movie.