It’s true in the past, that many scientists and engineers were independently wealthy (and yes, often though not always through inheritance). Others had patrons or got jobs as assistants to other scientists. More here: https://rootsofprogress.org/funding-models-for-science-and-innovation
Today there’s a set of institutions to support science and a whole career path based on them. What remaining important work is there that’s not being rewarded? I don’t know off the top of my head. My guess is that it’s something that most people don’t think about and that doesn’t have a prominent role in society—like science itself in the 17th/18th centuries.
On your second point, I agree that improving intellectual efficiency is an important part of progress. But I think that pretty much all of information technology, from the first writing system to the Internet, has been part of that effort.
Academic science works for learning about objective knowledge. It works less well for learning subjective knowledge like skills. If we look at the question like how one becomes a good software engineer, academia does pretty purely at answering the question.
We have inadequate equilibria where nobody is payed to solve it but it’s possible for someone who’s not payed to organize solving it.