Ah, Grasshopper, all words are metaphors.
Enterprise: Edsel at the Rouge.
The best part is that everyone in the show isn’t just speaking their own native language, or at least, not precisely. As the series goes on, John picks up expressions from his crewmates, and they likewise pick them up from him. Often, the nonhumans get a human expression not-quite-right, to humorous effect, and presumably John does the same thing without us noticing it. And John even starts gauging their moods by the fact that they’re using English words in particular contexts.
There’s also an episode in one of the later seasons with an alien of a species that can’t use translator microbes, but which is intelligent enough to learn languages quickly. Her first meeting with Chrichton consists mostly of her explaining this to him and telling him to talk a lot so that she has a body of speech to work with.
Forget Tamarian, or Klingon, or Ferengi, or whatever. Pretty much all Earth languages have increasing layers of abstraction built around not just metaphorical concepts and idiomatic expressions. Some of these concepts are easily translatable into other languages because of our shared human experience (off the top of my head, I can think of Chinese equivalents of “the pot calling the kettle black”, “save up for a rainy day”, and “no pain, no gain”), but others are references to history (“it was his Waterloo”), religion (“she saw the light”), literature (“I’ll be your Huckleberry”), philosophy (“they’re all shallow nihilists”), pop culture (“all your base are belong to us”).
(Side note: Did the series ever go into whether or not non-English Earth languages still exist within the Federation? Because if the universal translator had such problems with Tamarian, I shudder to think what it would’ve made out of the hundreds languages and dialects of good ol’ Terra Firma.)
And then they made thier job 1000x harder by failing to apply any context at all to what was actually being said. It was pretty obvious the it was <properNoun/name> and <properNoun/name> at <properNoun/location>, so why are you looking at definitions that do not fit that?
Galactic Standard. That’s why Picard has a “French” accent. 
It is likely that a spacefaring collective like the Federation has a common trading language that they all use. This would explain why non-Federation races can communicate with them in situation where they are not broadcasting through a comm device. The Feds, the Bajorans, the Ferengi, the Cardassians, the Klingons and many others would have traders and such who would be familiar with the language for trade and Diplomacy situations. For the rest, you have the UT to limp by the best you can.
Had the episode fully anticipated modern memetic dialects, the Tamarian language would have largely consisted of rapid flashes of apparently unrelated images on personal screens.
Technological quibbles aside, a problem with this type of language being used exclusively has become noticeable with those dialects: they change too quickly. New “vocabulary” arises every time something new and interesting comes along. If you are not immersed in the information flow, you quickly lose fluency in the current form of the dialect. From the episode itself, witness “Picard and Dathon at El-Adrel”–it’s a mutation of the original Darmok macro that is added to the language. If you happen to not visit icanhazstarship on the Tamarinet that day, you’ll be lost when someone uses it. I must assume that when the Tamarians record the new phrase, they’re basically updating KnowYourMeme.com.
French is stated to exist, although called “obscure.” At least one Native American language exists with an uncontacted Amazon tribe, according to Voyager. (Well, a tribe that was implicitly “uplifted” by magic white men from space, according to the same episode)
In your example, Obama knows a translator will soon be arriving. But in real life situations where there is no translator, dropping perfect grammar in favor of movie-indian-speak and pointing is commonplace. The point of speech is communication, after all: if perfect grammar produces worse communication than baby-speech and a pointing finger, grammar gets tossed.
Like I said, I haven’t seen the episode. I was just imagining at least one set of circumstances where it would be awkward/inadvisable to switch to “Baby Register”, even if it would solve a lot of problems.
Alternately, imagine Obama having to conduct the first “take me to your leader”-talk with incoming aliens. They speak english, but again, horribly childish english, picked up from listening in on broadcasts of children’s programming through the space waves.
Does Obama switch to baby-speak, thereby running the risk of insulting the spawn-parent of the alien and sparking an intergalactic incident? Or does he wait for the galactic linguist from the nearby university, who might be more competent at this sort of thing? Could go either way, I think.