I'm kind of amazed nobody has mentioned MAPS yet (
http://www.maps.org).
Psychedelics are a tool like any other. There is no such thing as "safe" use, which is why organizations like MAPS, DanceSafe, Erowid, etc all encourage the phrase "drug harm reduction." I have personally witnessed LSD destroy someone's life, and yet I have witnessed the same with alcohol (and am happy we have AA) and tobacco (cancer). The key, as with anything, is moderation and education.
That said, there has been a long trend of disinformation in the US, that has permeated all over the world. As a starting point, if people want to learn more about the crusade against cannabis (marijuana), check out Hank Anslinger and the Federal Bureau of Narcotics (https://en.wikipedia.org/wiki/Harry_J._Anslinger). For a more recent example, take a look at Rep Jared Polis questioning DEA Administrator Leonhart about why some drugs are illegal: https://www.youtube.com/watch?v=kFgrB2Wmh5s.
With regards to scientific inquiry into measuring the effects of these drugs, thanks to the efforts of Roland Griffith at Johns Hopkins (and others), we're beginning to overturn 40 years of prohibition with studies into the effects of psilocybin (shrooms) and MDMA (ecstacy) for end of life experience and PTSD therapy.
Some links to that research:
http://www.maps.org/research/mdma/
http://www.maps.org/research/psilo-lsd/
If this interests you and you ask "why hasn't this been done before?", I recommend searching for interviews with Rick Doblin, PhD (founder of MAPS) where he explains his long battle with the DEA, and how they eventually turned to the FDA, which focuses more on the science than the politics.
So yes, it is fair to say that there hasn't been much scientific research done into this, but to no fault of the scientists. I look forward to the next few years as the results of these studies come out and the US hopefully begins to permit these substances to be used in therapy.