For words which are commonly used in English (like "Paris") using the foreign pronunciation is guaranteed to sound pretentious.
English has a distinctive phonetic pattern, and switching to another phonetic system in the middle of a sentence for the purpose of pronouncing a different place name would sound odd and draw attention to yourself. Imagine an American speaker switching to a British accent every time he had to say "England". When speaking in an American accent, saying frahns instead of fraens (for France) is unbearably pretentious... even though frahns is the way it's pronounced in British English.
For more rarely used words (for example, small place names rarely mentioned in English), using foreign pronunciations won't be noticed. Nobody in America has ever heard of Ramat Gan, Israel, so pronouncing it the Israeli way (raMAT GAN) instead of the English way (RAMat GAN) won't even be noticed... but with American audiences, switching to American phonetics is always appreciated (using a hard American R instead of a gutteral or fricative will help people understand what you said).
Your assumption is correct. Natural languages are extremely redundant and compressible in sound as well as in orthography, and this has significant and obvious benefits: you can understand obscured speech, read obscured text, and, yes, get the sense of a word based on a quick visual hook rather than relying on a purely phonetic transcription.
English orthography reflects its countless generations of development. The spelling of a word may not correspond perfectly to its pronunciation, but to select a spelling that does correspond to a specific pronunciation naturally excludes some others. I've heard native speakers, for instance, who have different pronunciations for all of "to", "too", and "two".
Further, since the orthography often reflects the etymology, you can often make an educated guess about the meaning of a word you don't know based on the union of its visual and phonological components. If they were collapsed into one, you'd lose that extra information. This is just like how in hanzi there's often a phonetic component as well as a semantic component, and this does carry over somewhat to kanji even though the pronunciation is adapted to Japanese phonology.
These are all reasons why English spelling reform has never caught on, and likely will never do so. It's too widespread, and there are simply too many factors to take into account. Every language has its idiosyncracies, and to see them as flaws or try to fight them is sheer folly.
Best Answer
The problem is that there are a number of hidden assumptions behind this question that need to be picked away before the question can even be posed. Let me take them one by one.
This apparently refers to the English writing system, which is notorious for misrepresenting English pronunciation, as well as the pronunciation of any other language. English spelling is often said to be "not phonetic", though that's popular and not technical usage; phonetic science is actually about speech sounds only, not about writing.
The writing systems of every language, like their phonemic systems, are unique to and adapted to their own language. All of them are poor at representing sounds and sound combinations that don't occur in their own language; that's not what they're for, after all. What can't be pronounced can not be represented accurately in writing.
So you shouldn't look to other languages; you should look to phonetic science. The International Phonetic Alphabet is exactly what its name suggests -- a standard alphabet to be used to represent all human speech sounds, at the alphabetic (basically the phonemic) level.
No, that's not true. When Arabic speakers with Arabic names move to America, it's true that most Americans can't pronounce their names -- no matter how they're spelled -- not because of spelling, but because they don't know how to say many of the sounds. Arabic is full of sounds that don't occur at all in English.
When people who are not Japanese and don't have Japanese names move to Japan, Japanese people often can't pronounce their names, either, because they don't know how to say many of the words. Japanese has an extremely restrictive phonology -- virtually all syllables are Consonant + Vowel, for instance, with no real clusters and a small phoneme inventory -- and therefore Japanese speakers find many English words difficult if not impossible to pronounce.
(Squirrel is the English word my Japanese students found hardest when I was teaching ESL.)
There is a special syllabary in Japanese writing that is reserved for foreign names; but it does not represent their pronunciations -- it just indicates that they are foreign.
(My Japanese students had a lot of trouble with my last name, too -- the kana transcription of Lawler /lɔlər/ comes out as Roreru.)
No. As you see, this question isn't about the English language, but its writing system. The writing system is independent of the language; it's just one method of representing the spoken language.
The spoken language, the evolved language, the living language, the one that everybody learns before they go to school, whether they ever go or not, is the real language, and it would be the same language if it were written differently.
I will say that the English writing system is one of the worst-adapted in the world; however, much the same can be said of the Japanese system. And there are other things besides phonemes that writing systems need to represent.