AI and computers.
You know the trope that science fiction is "the present in the future", right? If one were to write a story set in the 3010s, it would most likely resemble the 2010s but with flying cars, super-tall skyscrapers, and robots. You don't tend to get too deep into the hard science of things.
Unless you're writing hard sci-fi. Then you do get deep into the hard science of things... except, in most cases, "hard science" really means "hard physics." It does not mean "hard psychology" or "hard neurology" or any of that. When you consider these things, stuff like flying cars no longer make sense. Humans have an absolutely terrible time with navigating a 2D plane at high speeds. Add another dimension, and you're looking at gigadeath. Things like decoding the genome in order to figure out diseases also requires supercomputing, otherwise would would have done it decades ago. Things like populating the outer solar system require advanced material science and cheap fuel to get to and fro— if we only ever put human minds to the task, we wouldn't reach the outer solar system for centuries. In fact, the reason why we haven't gone back to the moon is because it's so expensive and yields so little fruit. We did it just to say we did it, not to actually colonize the place.
We need some way to be able to think a thousand years in a day, to be able to find every pattern conceivable, etc. We humans can't do that, no matter how many of us there are; it's like trying to get chimpanzees to kickstart civilization.
Also: funding. Most parties on Earth don't care about space exploration. Right wing parties want to cut science in order to build up defense; left wing parties want to cut science in order to build up welfare. We've had plenty of Democrats and Republicans ever since 1966— the peak of NASA funding— and yet NASA's budget has only ever decreased. It's gotten to such a ridiculously bad point that we were cheering for 2016's "massive" NASA budget, despite the fact it's still one of the 10 lowest budgets ever. In fact, one reason why I don't comment on your opposition to Republicans is because it was Clinton and Obama who buttfuck't NASA's budget the worst. Then again, it was a Democrat who gave it its largest budget— Johnson, though he did it mainly to achieve Kennedy's wish of putting a man on the moon.
In the end, it's been the computer that's kept us from post-industrial stagnation, as we plucked all the low hanging fruit by the '60s (hence why some people think Gen X, Y, and Z haven't had their own 'Moonshot' moment). I don't think Heinlein (or most early sci-fi authors) foresaw just how many of these sci-fi innovations would be tied to computing power and funding. It seems that most people think "future = more advanced", just because. In fact, 2016 could have been just as advanced as 1966 if computers stagnated around that time, and computers could have stagnated by way of no one funding their development. We needed computers to go to the moon, as weak as they were.
We could still be in medieval times if no one funded the Renaissance or global colonialism. NASA could have created smartphones in 1970, and no one would have them if private industry didn't fund their development and marketing.
We won't have robot butlers until computers can autonomously navigate 3D space well. We won't have an end to disease until we are able to attack viruses, bacteria, and cancers at the root.
Of course, combining computers with money might ease all that— create wealthy artificial intelligences, for example.