I think you are misunderstanding the role of the FDA. The FDA does not engage in research, and hasn't for a long time (if ever). The FDA is strictly a regulatory agency. They approve drugs and food additives, and devices for use in the USA, but the research is ALWAYS done by someone else. In order to secure FDA approval for a drug or treatment , you have to present evidence that it is statitical superior to a placebo, and is 'safe' relative to the intended use.
If someone wanted to do research into the efficacy of coffee enemas, and could show they are safe and effective in peer reviewed, double blind studies, I don't think the FDA would have any trouble approving. The problem is there is no money to be made from such an approval (no drug patents would be involved), so no one is willing to fund the studies that would be necessary.
Let me give you an example. For literally hundreds of years, Cascara Sagrada has a record of safe use as laxative. The FDA didn't approve it's continued use because there are no clinical studies to demonstrated both safety and efficacy. The FDA stated quite clearly that Cascara was approvable, as long as the approval criteria could be met. A reasonable sized clinical study probably costs upwards of $10 million. There simply isn't enough money to be made from the sales of Cascara Sagrada (and there are no patents to be issued for it) to justify the expense, so the requisite clinical trial isn't going to happen. Cascara Sagrada is no longer approved by the FDA as a laxative.
Food Supplements are a whole other kettle of fish, and basically Food supplements operate on the opposite set of assumptions. The FDA does not approve them, they only ban them if there is demonstrated evidence that they are unsafe.
So the real question you should be asking is why the National Cancer Institute of the National Institutes of Health hasn't done any research. They are the researchers, not the FDA.
In general the medical community isn't opposed to alternative treatments, the problem is in our society, if you use a treatment that doesn't have proven efficacy and safety (FDA approval), and the outcome is sub-optimal, you get sued and are likely to lose. So as long as you can show via well run clinical study that the alternative treatment is superior to placebo, you can probably get approval. Very few alternative therapies have been through double blind, peer reviewed, clinical studies. Given the lack of such clear evidence of effectiveness for most 'alternative' therapies, they are going to remain outside the mainstream.
Medicine has often been well behind the 8 ball on reality. The physician who suggested that many stomach ulcers were the result of a bacterial infection was almost laughed out of the profession. Fortunately for him, there were a few people who belived him, and did the clinical studies to establish that conventional wisdom was wrong, and appropriate antibiotic therapy really does cure most stomach ulcers. Once the evidence from peer reviewed, double blind clinical studies was clear, the FDA approved the treatment and the drugs.