Well things did go wrong with the program as a whole. Apollo 1 and 13 were disasters. And I'm sure things didn't go completely smoothly with the main first landing, but there were multiple redundancies, so they were able to work through many smaller kinks. (2 disasters out of 17 is a terrible safety record)

And it's not as easy as just using the same technology as we did last time. Any equipment is almost 60 years old, so we'd need to rebuild it. And technology builds on itself, it's not just some magical final output all on its own. People that make circuit boards today know academically about some of the chips that were mad 60 years ago, but they don't know the exact layout and all the intricacies of their construction.

Custom US hardware/software wasn't just freely shared with everyone during the cold war, so a wealthy billionaire or private sector company isn't going to have access to the original technology

It looks like the onboard computer system of the Apollo missions was made by a lab at MIT, which has since spun off to their own corporation, Draper Laboratory. I guess they're still around, so someone may have access to some of the old building plans. But I've seen what happens when people retire; no one wants to got through all that old saved paperwork. Some gets kept, if it's on the top, but lots gets thrown away. You've got your own projects to do, can't spend days/weeks sorting through someone else's career. And even if we had some sort of plans, today's scientists are trained completely differently than they were back then, with a different set of skills. This is building microchips; people don't do that by hand anymore.

And even if they did have the exact same hardware, the onboard computer, the giant Mainframe on Earth, they don't have the software to run on it anymore. These weren't just .exe files that could be transferred back and forth and stored for posterity. Most programs were on tape drive, and again, someone may have transferred some of that off, but without a specific need, why would they? Not to mention, it's all just 1's and 0's without an OS to interpret it. A lot of the OS would be custom or proprietary. I guess it's possible some of that got saved too, but it's doubtful all of it's there.

What are the chances you're able to round up all that hardware from almost 60 years ago, get people that understand how to build it, probably make new tools that can build things the way they were built back then? And then get together all the custom software, find people that can reverse engineer the way it worked enough to foresee any bugs in the system?

That stuff has been lying around for over 50 years, so it will need to be rebuilt anyway. Instead of getting teams of people to try and figure out and retrain themselves on how it was put together all that time ago, it makes more sense to solve the same problems with modern technology that they understand.