Homeopathy is as easy or hard to assess using double-blind methods as any other medical treatment. Administer the homeopathic medicine to some and placebo to others using double blind randomization protocols. Yes, funds HAVE been allocated to study such treatments, and it is these studies that the article reviews.
Homeopathy has ZERO basis in science. There is NO systematic, objective evidence it is an effective treatment for anything.
Practitioners who peddle it are at best frauds and at worst guilty of manslaughter (for those patients who may die because they have suckered into a homeopathic remedy as opposed to a science-based one), and people who use it are fools.
I take it that you are using the 1796 original theory as the definition of homeopathy. I would like to just use the Greek word roots, and make a fresh start with the concept evoked. Science was pretty new back then, and we were still doing leech therapy for a lot of stuff as "mainstream medicine". We were also using heavy doses of arsenic and such as "medicines". At that time, it is likely that an ineffective placebo was better medicine.
The physical realities of a well-financed, adequately-sized and properly controlled double-blind investigation are such that studies of low-dose therapies will be invisible, statistically. With patient mobility and the cost of personnel, you have to have a dose with an effect that is observable within a small time window. Those constraints do make an objective test of a homeopathic "cure" practically impossible.
Personally, I don't believe there is sufficient plausible coherence with the body of experience we have, or the knowledge we have, to make funding a study of the original three principles of homeopathy a good use of anybody's funds.
However, taking a more liberal view of the term "homeopathy", the idea of something that is like the cause being a possible cure, if applied at a different dose, has some merit. The scientific basis of believing there could be such a relationship in some illnesses or disease states, is real enough. We know about dose-response curves and threshold effects. We know many things in large doses become problematic in our biological systems, even water can cause illness if you drink too much. Many things classed as poisons at one dose, usually very high, are essential to health at another dose that is compatible with our design or nature.
We have several examples of this already accepted as good medical practice. Radiation treatments for cancers, for example. Even very low doses of radiation are thought, generally, to cause cancer. Very high doses, below the level of immediate fatality, are known to result in certain cancers at a very high statistical probability. But we have found a certain range of doses to be therapeutic and useful in treating cancer. In this range, there is still a known risk of causing cancer, but it's a lower risk than the very high certainty of death from an existing and diagnosed cancer.
I have here disputed the merits of the OP study as being anything more than a review of studies, which I might discuss individually as to merit or intent. . .. but certainly I do not expect any study to show a positive result, as we define "homeopathy" as one early nineteenth century theoretician who formulated a hypothesis I consider worthless on its face. I would expect some results comparable to placebo effects.
But I would like to see the general idea of treatments which go with our biochemical systems, exploiting some known dose-dependent response curve studied with actual scientific methods.
With the current statistics of medical malpractice among mainstream providers, and the claimed pervasive side-effects or mortality from even prescribed pharmaceuticals, I would not want to see a lot of mob mentality for lynching any kinds of "medical" practitioners. As in the days of the medicine show fraudsters of over a hundred years ago, it still a good idea to at least be alert, for consumers of medical services and substances to be sorta light on their feet, with a "caveat emptor" wariness. I'd rather not incur damage than try to recover damages in legal tort.
So I sorta think your enthusiasm for bringing charges against homeopathic fraudsters runs the wrong way. The people who turn to them are largely adverse to perceived risks in the mainstream practice of medicine, and many have been failed by the mainstream treatments already. They really aren't a lot different from the people who rejected the leaches and the arsenic of the nineteenth century. If you want to help them, the best way is education. And isn't that what you do?