Assuming that humanity even survives the many species ending trials that still await, this is favoring a single or small cluster of humans from a singular shared monolinguistic culture being the genetic/survival bottleneck that humanity passes through.
Otherwise, linguistic research shows that dialectical divergence can happen remarkably quickly, as in the case of American English, which is showing signs of increasing linguistic balkanization that lines up with its splits into seemingly increasingly isolated cultural confederacies.
A world reduced to one universal language to the exclusion any other could only come about in one where inequality does not exist due to the condition of economic scarcity having been eradicated, along with the concept of ethnic identity. Otherwise, there will always be a method, if not an incentive to exploit the inequality to create resentment, then the resentment acts to resist the will of the authority, such as learning the language of the overlords.
Simple convergence and economic convenience in a fully globalized world.
Unlike what @signal11 implied, I’m not suggesting any sort of imperialism. My thought is that, warfare cataclysms aside, 1000 or 3000 years from now some mix of what’s now termed “English”, “Mandarin”, and perhaps “Bengali” will be spoken by everyone everywhere. With minor admixtures from Spanish, Arabic, and whichever language emerges as dominant among Africa’s burgeoning population.
The (WAG) 35 dialects common in England 600 years ago could survive because they didn’t really interact with their neighbors. That’s been almost entirely swept away in the last hundred years because now those folks all do interact with each other and with the outside world.
I predict the same process will occur on a global scale. Yes, there will be regionalisms and accents and such. And some ebb and flow of this integration over timescales longer than a single human lifespan. But the language regions will grow ever larger because everyone will be well-connected and interacting over a broader geographical scope. Which will eventually spread to have covered the whole planet.
As a microcosm, the SDMB started out as a purely local Chicago phenomenon. At its peak we had significant participation from all over the world. And still have a decent amount.
While this may well come to pass at some distant date, I think it’s unrealistic to expect that this global lingua franca will wipe out all other languages. People will speak the global language, with varying degrees of fluency, and their own native language(s).
In the distant future, with genetic upgrades and computer upgrades integrated into our brain, I’d expect that spoken languages are just something you install as fits your fancy. Most communication would probably be some constructed language that’s ideal for digital transmission.
I claim no expertise in the matter, nor am I particularly invested in my opinion. I was just extrapolating recent (last 2-4 centuries’) trends forwards to their logical limit. Which limit is often actually illogical.
As you say, even setting aside ugly politics there may well be a natural obstacle to how far that convergence goes. Megacities and automobiles mean that here in the 2020s 150 miles away is not far and villages that far apart will speak the same accent of the same dialect of the same language, and may even be part of the same municipality. Quite different from the situation in e.g. 1200s Europe.
But the Earth is still a big place and absent Start Trek teleporters even a comfortably upper-class human in the year 3000 will probably still be dealing with people within a couple / few hundred miles of home more frequently than those ~12,000 miles away at their antipodes. At least in person; if we’re all living in the Matrix by then things might be different as distance becomes fully meaningless.
But assuming no ST transporters and no Matrices, I could see the convergence to a single tongue stalling at some point due to the maximum size of our personal monkeyspheres even after generations of world-spanning cultural contact and the sort of open-eyed education that goes with that.
We here today won’t live to see the “end state” in either case.