Personally, I think it's exactly the opposite issue. Academia became too involved in social conflicts and found itself in the crosshairs. Think about what else was happening in the 70s-80s? Lots of social unrest, especially involving young students advocating radical ideas. What easier thing to attack than their radical schools, teaching them that reality doesn't even exist?
But more to the point, let's assume your argument is true. Academics can't really go back to the positivist position. Many of those results were trash. We don't want to stay with postmodernism either. It's not total garbage, but math is way easier to verify than some dude's stupid interpretation of some other dude's random babbling. Plus, you can make computers do math really fast. You can't make a computer analyze text in a postmodernist framework (yet). So, over the past 30ish years what you'd probably want to see is what's been happening: Academics finding a bunch of middle ground between the two where they can still be productive, without losing the human side of PM.
I feel like some people wear "nobody understands me" as a badge of distinction. This is wrong. If nobody understands you, you're a poor communicator.
> I think it's an argument essentially captured in the term "ivory tower", which began being used for academics in the 1800s. It's a pretty old argument.
I suppose it is an old argument, but I don't think that invalidates it. I think it's always been true and what we're seeing is the gradual unfolding of the consequences. Of course I still do believe that the ivory tower has become more tower-like in recent years, especially in the humanities. Why is Jordan Peterson so popular? Where are the public intellectuals who are not crackpots or misogynists to answer the deep life questions of all these disenchanted people who otherwise flock to people like him?
Science and engineering papers are impenetrable too, but those at least yield end products that have results in the world outside academia. At the most base level academia can always petition for their continued existence on the grounds that they are necessary to maintain military superiority. That's a narrow rationale, but if all else fails it's not wrong and it at least grounds academia in society somehow.
I think academia has to either come down from the ivory tower or the tower will fall when the masses inspired by a tweet by the first American Emperor lynch them all for promoting vaccination.
I agree that we can't go back to the positivist position, but it's also not clear to me that positivism is wholly wrong. It seems to work really well in certain domains. What we need is to examine the domains where it doesn't work and decide if we need to refine it, expand upon it, or realize that its domain is in fact limited and come up with new methods for other domains. "Anti-method" is not a method, so that's not an answer. That's giving up on the question.
The reason I'm a bit peeved in these replies is that I do have a powerful sense that the humanities in academia have lost their relevance by going down a path that is increasingly insular, alienating, and unproductive, and that this has had a role in ceding the cultural ground to reactionaries, fascists, and other kinds of actively destructive irrationalists. That's why elsewhere I make the analogy to string theory, a fad that seems as if it's been fruitless and has derailed physics.
In short I've blamed pomo for why there is a resurgence of racism, reactionary ideology, and stuff like the anti-vaxx movement. Not only does this stuff result in an intellectual class that speaks gibberish that nobody but them understands, it also at least superficially sounds as if it's legitimizing the idea that "all opinions are of equal merit." That means if I don't want to vaccinate my kids because Alex Jones said so, my opinion is equal to that of an epidemiologist because cultural relativism.
Edit: I realized there's a more pointed way of saying what I said above: I am not sure you can try to argue that all cultures are equivalent and equal without implicitly asserting the same about all ideas within one's own culture. This is because cultures and boundaries between them are fluid. So if it isn't possible to criticize cultures, it's also not possible to say that Richard Spencer's ideas are worse than Martin Luther King's or that Alex Jones' opinion on vaccination should not be equal to that of an epidemiologist. Nothing is true and everything is permitted.
My observation has been that the left prototypes nonsense and then the right deploys it at scale. So the left first pioneered relativism and critiques of reason and evidence, but it's the right that has run with these ideas and used them to re-legitimize racism and lead a renaissance of interest in traditionalist monarchy. Maybe the left should stop prototyping nonsense to begin with if for no other reason than to stop giving weapons to those who ought not have them. It's the same reason you don't give plutonium to ISIS. I truly do not believe that dullards like Richard Spencer or Pat Buchanan have the capacity to originate a cultural zeitgeist any more than ISIS can build an enrichment centrifuge, but they sure can use the final product if it's handed to them.