Consider in 1969--much less going back to when many of the design decisions were made. (And by "no" here, I mean no in anything approaching mainstream.) No electronic calculators, just barely color television, mostly rotary dial telephones. Moore's Law had only recently been coined. No PCs of course. No Internet in any meaningful sense.
All of what you say is true, however it's not as bad as you might think. Once upon a time were these magical devices called "mainframes" [1], and in the 1960s they were quite powerful (for that era).
Most engineering work was done in FORTRAN, and it ran very efficiently on the hardware. There were (usually) no CPU cycle sucking GUIs to slow down the computers.
As a high school student in the early 1970s I was privileged to take a summer course at the Goddard Institute for Space Studies [2] where they had an IBM 360/95 mainframe [3] for the scientists to take turns using (job entry by punched cards, job output by paper printout).
It's been so many years, and it was only casually explained to me, but I think NASA used three other 360/95 mainframes (the IBM top of the line at the time) located at the Goddard Space Flight Center [4] in Greenbelt MD to track the Apollo missions. I think these ran the same program more-or-less in triplicate (but there was no hardware for syncing). I think NASA also had an IBM 7094 [5] running an independently written program as a backup in case something went wrong with the S/360 computers.
Trust me, these computers were very very capable for the time. It's not like the primitive computer onboard the Apollo LEM. Mainframes were quite up to the task.
I've programmed on an IBM 360 in FORTRAN :-) so I knew they had computers. NASA has always been one of the big US government buyers of computer technology. The technology they had to work with on the ground was certainly relatively more sophisticated than what they could fit into the spacecraft and expect to run reliably.
But color TV had been widely available for about a decade. In fact, I watched the 1969 moon landings on my parents 1961 color Zenith. (They had rotary phone well into the 80s, however.)
My mother had one of the early SCM Marchant electronic calculators in her lab http://www.oldcalculatormuseum.com/scm240sr.html. I don't remember the exact date but looks like it looks like it would have been late 1960s as well. I remember how laughably slow it was doing square roots; you could watch it going through some sort of successive approximation algorithm.
"By the late 1960s they did the technical ability, not to mention the requisite madness, to send three guys to the moon and back. They did not have the technology to fake it on video." https://www.youtube.com/watch?v=sGXTF6bs1IU
Great video. For others wondering, it's a video that debunks conspiracy theories about faking the moon landing by saying it was technically possible to fly to the moon but not to fake it. It goes into the logistics of how a moon landing would be faked (film capacity and technical capabilities of cameras in the 60's).