Rather than the the thrilling explanation that a consortium of paper/wood processors and tobacco concerns pushed rivals out of the field, the answer likely lies in the laws of the Progressive Age.

The first laws that set about making cannabis illegal began with various food and drug acts, which required food and drugs to be properly labeled. Previous to this, snake-oil salesman could sell anything, to anyone, containing anything, without disclosing what was inside. Medication was a badly regulated field, particularly in regards to habit-forming drugs, and absolutely in regards to outright poisons sold as medicine.

The first real regulation to impose limits on doctors, pharmacists, and medicines prescribed was introduced with the Townes-Boylan Bill in New York State. This bill was critical in preventing doctors/pharmacists from just prescribing their patients anything, for anything, at any time. It began to put limits on what could be prescribed, and in how much quantities (including, crucially, hypodermic needles). The good intentions of this bill were to make sure that doctors and pharmacists underwent some kind of oversight and regulation, particularly in regards to habit-forming medications.

This New York state bill set the stage for a national law, The Harrison Act, introduced by Rep. Harrison of New York. This bill did two very critical things. First, it allowed the government to tax coca and opiates. Secondly, it allowed for government regulation, on a national scale, of medicines. The legislative goal of both of these bills was to tighten the governments ability to regulate the medical industry, including both pharmacists and doctors, while also allowing them to tax industries that had previously been un-taxed. At this time, there were racial overtones towards certain drugs, but there were serious issues of addiction, and almost no one understood the process of addiction or recovery, beyond the barest analysis.

Crucially, while these laws were concerned with cocaine and opium, they now allowed states to determine what was a poison, and what could therefore be not be sold. Cannabis was seen as a habit-forming drug, and was quickly placed on lists of poisons, particularly in western states. This preventing it from being used alongside coca or opium, as it did not have the same immediate medical concern.

From that position of progressive intentions, you have states largely making their own lists of poisons, their own methods of determining what can or cannot be sold or regulated, and what may or may not be determined to be a habit-forming medication. In any case, cannabis at this time was routinely determined to be a poison, seen to be habit-forming. There is likely no deeper answer to this question than cannabis was seen to be habit-forming in a way similar to opium or cocaine. It would have been utilized in various snake-oil tinctures in a way similar to opium or cocaine, but without the immediate and obvious analgesic or anesthetic effects.

Ultimately, the Uniform State Narcotic Drug Act was passed in 1934. This brought a national answer towards what was legal, and what was not legal, from coast to coast, as well as supplying legal authority that the Harrison Act lacked. Opium, Coca, and alcohol would have had medical and/or cultural existences behind them that would have afforded them deep analysis towards specific regulatory measures. Cannabis was mostly new, mostly unknown, and almost totally unused by any medical practitioner. Furthermore, since it had been designated, legally in several states since 1915 as both habit-forming and poisonous, it would not have been difficult at all to place it on the list of prohibited drugs. In regards to tobacco, timber, or paper interests, there appear to be absolutely no cannabis lobbying interests at this time, so Spectres like Harry Anslinger likely wouldn't have worried about the commercial rivalry of a product with zero infrastructure and zero production base.

It would have been banned because it was seen as, likely, a dangerous and habit-forming drug, and by the time came to designate it as such, the legal muscle for that argument had been in place for years, if not decades. It was given that designation during the Progressive Era, no one ever re-examined it for medical use in the way they did for cocaine or opium, and that was pretty much that.

Sources: https://www.nytimes.com/1914/07/30/archives/topics-of-the-times.html https://www.nytimes.com/1914/01/26/archives/to-make-it-harder-to-get-habit-drugs-townsboylan-bill-at-albany.html http://www.druglibrary.org/schaffer/Library/studies/vlr/vlr3.htm https://www.economist.com/special-report/2001/07/26/how-did-we-get-here