Have there been any movements/tendencies to remove definite and indefinite articles from English in the recent history of English?

Although I have no certain knowledge of whether there have been specific "movements" to remove articles from the language, it is almost impossible for a native speaker to conceive of the existence of such a movement. Removing definite and indefinite articles would amount to the destruction of one essential element of the language. The presence and usage of articles in English is absolutely fundamental to the very structure of the language. Don't forget that language is both a reflection of the way one thinks, and (as we are now learning more and more) a formative force in the way one thinks. What this means is that the very thought processes in the brains of native speakers of English are wired to operate along pathways that require these articles. Pulling the articles out would be like turning off your headlights while driving your car at night; you can't find your way without them.

To address your examples of where articles are omitted, each of these cases has specific reasons and justifications for their removal, and the absence of the articles serves specific purposes. In the case of song titles, the reasons are essentially poetic ones, in which evocative and creative use of the language is paramount. In the case of computer program menus, the absence of articles is to highlight the function of the item listed in the menu. In the case of dictionaries, articles are omitted because the words themselves are the objects of attention, instead of the items to which the words refer. I could go on, but I think you see my point.

There are languages (French, for example) which utilize articles in more syntactical places than English does. For an English speaker learning French, the additional usages are initially challenging, because our mental language wiring doesn't include those pathways. But they are essential to the structure of French, and dropping them would make no sense to a French speaker. Dropping the "additional" uses would disrupt the language just as much as dropping all articles would disrupt English. It just wouldn't be feasible.

Existing English language Movements and Campaigns

Here is a list but by no means extensive:

• Cut Spelling In the 1970s the Australian psychologist Valerie Yule found that many irregular spellings arise from redundant letters. These are letters which mislead because they are not needed to represent the sound of a word. Writers then cannot tell from a word's pronunciation which letters its written form requires, nor where to insert them, while readers are likely to mispronounce unfamiliar words containing them. A group within the Simplified Spelling Society therefore decided to explore which letters are redundant in English, and the effect their removal has on the appearance of the resulting 'cut' text. This Cut Spelling (CS) is now used for the rest of this column and for the next in order to demonstrate that effect.

Esy readng for continuity.

One first notices that one can imediatly read CS quite esily without even noing th rules of th systm. Since most words ar unchanged and few letrs substituted, one has th impression of norml ritn english with a lot of od slips, rathr than of a totaly new riting systm. Th esential cor of words, th letrs that identify them, is rarely afectd, so that ther is a hy levl of compatbility between th old and new spelngs. This is esential for th gradul introduction of any spelng reform, as ther must be no risk of a brekdown of ritn comunication between th jenrations educated in th old and th new systms. CS represents not a radicl upheval, but rather a streamlining, a trimng away of many of those featurs of traditionl english spelng wich dislocate th smooth opration of th alfabetic principl of regulr sound-symbl corespondnce.

• English-only movement also known as Official English movement, refers to a political movement for the use only of the English language in official US government operations through the establishing of English as the only official language in the United States of America.

• Plain English Campaign (UK) Since 1979, we have been campaigning against gobbledygook, jargon and misleading public information. We have helped many government departments and other official organisations with their documents, reports and publications. We believe that everyone should have access to clear and concise information.

• Plain Language Action and Information Network (PLAIN) a group of federal employees from many different agencies and specialties who support the use of clear communication in government writing. Our goal is to promote the use of plain language for all government communications. We believe that using plain language will save federal agencies time and money and provide better service to the American public.

• ProEnglish Founded in 1994 it is an American non-profit lobbying organization that supports making English the only official language of the United States.

• SaypYu The Spell As You Pronounce Universally project promotes "the simple universal phonetic alphabet" which is intended to facilitate a quick and convenient writing system for verbally penetrating foreign situations and pronouncing unusual place-names reasonably quickly and accurately.

• Simplified Technical English It offers a carefully limited and standardized subset of English. It is now officially known under its trademarked name as Simplified Technical English (STE). Although STE is regulated for use in the aerospace and defense industries, other industries have used it as a basis for developing their own controlled English standards.

The Simplified Technical English specification consists of two Parts:

• Part 1: Writing Rules,

• Part 2: Dictionary. Writing Rules

The Writing Rules specify restrictions on grammar and style usage. For example, they require writers to:

1. Restrict the length of noun clusters to no more than 3 words
2. Restrict sentence length to no more than 20 words (procedural sentences) or 25 words (descriptive sentences)
3. Restrict paragraphs to no more than 6 sentences (in descriptive text)
4. Avoid slang and jargon while allowing for specific terminology
5. Make instructions as specific as possible
6. Use articles such as "a/an" and "the" wherever possible
7. Use simple verb tenses (past, present, and future)
8. Use active voice
9. Not use present participles or gerunds (unless part of a Technical Name)
10. Write sequential steps as separate sentences

11. Put commands first in warnings and cautions, with the exception of conditions

    • SoundSpel is an English language spelling reform proposal. Its origins date back to 1910

Example:

The Star by Herbert George Wells

It was on the ferst dae of the nue yeer the anounsment was maed, allmoest siemultaeniusly frum three obzervatorys, that the moeshun of the planet Neptune, the outermoest of all planets that wheel about the Sun, had becum verry erratic. A retardaeshun in its velosity had bin suspected in Desember. Then a faent, remoet spek of liet was discuverd in the reejon of the perterbd planet. At ferst this did not cauz eny verry graet exsietment. Sieentific peepl, however, found the intelijens remarkabl enuf, eeven befor it becaem noen that the nue body was rapidly groeing larjer and brieter, and that its moeshun was qiet different frum the orderly progres of the planets

• Speak Good English Movement (Singapore) The campaign aims to discourage the use of Singlish and encourage the use of a more standardised form of English (i.e. generally modelled on the British standard).

And then frankly I gave up.

As far as I can tell there has never been nor will there ever be a movement to eradicate articles from the English language.

EDIT: For those whose curiosity has been whetted, may I recommend reading this answer by Alain Pannetier who gave a splendid summary on the history of the indefinite article here: https://english.stackexchange.com/a/35385/44619

• No, there is no organized movement to eradicate articles in any variety of English
• There is no unorganized trend of the loss of the article, except in very small communities, like 'headlinese', or English pidgins
• Whether one uses an article is a complicated matter that is difficult for non-native speakers to master
• There is no central authority for the English language to which one could appeal to have the existence of articles removed. Language rules change organically (Frankly the same is true of French which, even though it does have an ostensible body to arbitrate such rules, no one actually follows them except pedantic school teachers) .

So no, there are neither movements or tendencies for articles to fall away. No one speaks in headlines.