20% is
way too high. Even ignoring the (important!) human factors, that sort of failure rate would raise the expense tremendously all on its own. We are finally seeing a glimpse of true reusable rockets, which are the only way to do things in space at anything like a reasonable cost. A 20% failure rate means your reusable rockets can't be reused very much.
Along similar lines, even if you ignore the fear and grief factor, a 20% fatality rate means you'll never create experienced astronauts.
I also really doubt that putting the risk that high would be particularly useful. Even the worst non-man-rated rockets out there have a failure rate of something like 10%, and those failures generally wouldn't kill the astronauts if their spacecraft had a launch escape system. The Space Shuttle's fatality rate was about 2%, and that was only because it was a vastly over-complex, fragile machine with no realistic abort modes in many phases of flight. No other spacecraft made or planned could fail in the ways the Shuttle did.
A government effort probably will be expensive, but only because they're slow to adapt. It will probably be quite some time before we see a(nother) reusable government rocket.
However, a private effort won't go anywhere, because there's no business case for a moon base, nor even a "dream big" case for an Elon Musk type figure. (Mars is a better target by nearly every measure for the second one.)
The best bet IMO would be a public-private partnership, with governments providing the basic goals and funding, and private companies providing the technology and services.