Yeah, I agree that the EMH holds true more for incremental research than for truly groundbreaking ideas. I'm not too familiar with MCMC or Bayesian inference so correct me if I'm wrong, but I'm guessing these advancements required combining of ideas that nobody expected would work? The deep learning revolution could probably have happened sooner (in the sense that all the prerequisite tools existed), but few people before 2010 expected neural networks to work so consequently the inefficiencies there remained undiscovered.
At the same time, I wouldn't denigrate research that you might view as "incremental", because most research is of that nature. By this I mean, for every paper published in the ACL / EMNLP conferences, if the authors hadn't published it, someone else would almost certainly have published something very similar within 1-2 years. Exceptions to this are few and far between -- science advances via an accumulation of many small contributions.
True, I guess a more precise statement is "most problems that are important and solvable are already solved". There are lots of small gaps in my research as well, like "what if we make a minor adjustment to method X" -- whatever the outcome, it's below the bar for a publication so they're generally left untouched.
To be fair, almost nobody considered a pandemic to be a serious possibility prior to 2020, so it is understandable that pandemic preparedness research was a low-priority area. There may be lots of open and answerable questions in unpopular topics, but if the topic is obscure, the payoff for making a discovery is small (in terms of reputation and recognition).
Of course, COVID-19 has proven to us that pandemic research is important, and immediately researchers poured in from everywhere to work on various facets of the problem (e.g., I even joined in an effort to build a ventilator simulator). The payoff increased, so the inefficiencies quickly disappeared.
Now you can argue that pandemic research should've been more prioritized before. That is obvious in hindsight but was not at all obvious in 2019. Out of the zillions of low-priority research areas that nobody cares about now, how will you decide which one will become important? Unless you have a time machine to see into the future, it remains a low-payoff endeavor.