This (the machine invented by the famous Chinese author, Lin Yutang, and described on the first page [first four paragraphs] of the Wikipedia article here) is probably the closest the Chinese ever got to decomposing their script into an "alphabet" consisting of "letters" (recurrent graphemic elements that can be combined in a principled way to form all of the characters / morphemes in their writing system). You'll note that it didn't really work during their presentation to the Remington Typewriter Company executives. The press conference demonstration they had the next day was probably of the carefully rehearsed, staged, orchestrated sort designers of Chinese information processing / technology software and hardware often present (the kind documented by Li-ching Chang in her film made at a vocational high school in Beijing), not one prepared to respond spontaneously to tasks posed by the audience. Judging from my own experience with Chinese software and information processing / technology developers over more than a quarter of a century, this may have been what went wrong when Lin presented his typewriter to the Remington executives: they asked him (or his operator) to type something impromptu. Incidentally, the development of this fatally flawed typing machine left Lin — whose books were bestsellers in America — bankrupt.
The "typewriter" described on the second page (fifth paragraph: "Another kind of Chinese typewriter") section of the Wikipedia article cited above is the only kind of machine for writing Chinese that achieved fairly widespread use. (Most of the typewriters shown here are of this sort.) It was basically a limited font of about two to three thousand of the most common characters, with hundreds or thousands of more obscure characters kept in boxes nearby, to be laboriously sought out when needed (most typists just wrote such characters in by hand [if they knew them; but usually they were simply copying from a printed page or somebody's handwritten draft anyway — even now, except with pinyin-inputting systems, Chinese have not benefited very much from touch-typing] rather than try to find them in the boxes). The Wikipedia article claims that "good operators were able to type around 70 words per minute." First of all, this probably means "characters," not "words" (which are largely disyllabic). Secondly, this could only have been true of a highly skilled operator presenting a carefully prepared and practiced text without any unusual characters (i.e., beyond those in the main tray). The typists I observed using these machines in Taiwan, China, and at the UN back in the 70s and early 80s — all professionals, not casual typists — seldom exceeded about 10-12 characters per minute under the best circumstances (only common characters found in the main tray, and working from clean drafts or copying from printed materials).
Many of the difficulties outlined above have continued even into the computer age, which accounts for the (should I avoid using "literally"?) thousands of different inputting systems that have been devised during the past three decades. The vast majority of individuals, both for short text messaging and for word processing with computers, now use various types of romanized inputting, with those methods that take advantage of word segmentation being the most efficient.
Thanks to Michael Carr for the first Wikipedia reference.