1. Even if we start spelling English with the International Phonetic Alphabet, we will never be able to represent spoken English with complete accuracy. Every language, even more "phonetic" ones, like German and Spanish according to the article, has discrepancies between spoken and written forms. This comes about both from change over time and change across regions. How will you represent "talk"? With a closed aw-sound, like in England and New York, or with the more open ah-sound of the rest of North America? Will my three separate pronunciations of Mary, marry, and merry be taught as wrong if simplified spelling means there are no longer three different vowels (long a, short a, short e) in these words? Even the transcription on the IPA's own page chooses the r-less pronunciation of international, taking one side of a division that spans the entire Anglophonic world.
Language change over time is also a challenge to simplified spelling. Everytime we look at a word and realize we (or some of us) have changed how we say it, do we change spelling accordingly? It seems like simplified spelling will only reflect the pronunciation of those who enact it, at the time they enact it. And as for change over longer periods, simplifying spelling means Shakespeare--writing in early modern English and thus a challenging version of the same language we speak--will instantly become for students about accessible as Chaucer or even Beowulf.
The goal of matching spoken with written English will never be met because they serve two different purposes: Spoken language matches the varying situations of life, while written language holds them all together just close enough to preserve a fragile unity. We all have multiple versions of spoken language: public-speaking, job-interview, talking to grandparents, chatting with friends, talking to pets, cursing wayward computers, etc. And this doesn't just entail variance in vocabulary ("stupid" vs "ill-advised"; "not my F-ing problem" vs. "perhaps you should check with..."), but pronunciation as well ("gonna" vs. "going to", "nah" vs. "no", "yeah" vs. "yes"). And of course the fine line between what constitutes a different pronunciation vs. a different word (Southern "cuss" vs. standard "curse") itself only highlights the difficulty of trying to nail down standard English pronunciation into a simplified spelling.
2. Moreover, simplified spelling rests upon the idea of representing spoken speech in written. Certainly this has been the goal of writing throughout history, but in this age of literacy and electronic access to written data, the relationship between a word's spoken and written versions is more complex, with each affecting the other. E.g., when I see the word pin, my mind thinks of the word as it sounds when I say it. Yet when I hear a word spoken, my mind really does three things: 1) it registers the sounds it heard and classifies them based on the categories I've already formed (learning more languages here definitely broadens the mind), 2) it recalls the spelling of that word, and 3) it recalls how I pronounce it (the 'right' pronunciation, in a purely referential sense). So when I hear my New York friend M say pin, I hear the sounds in my head, imagine the word 'pin', and automatically compare what I heard with how I say it myself. Ah, but when most of gaetanus' family says pin, I know that's how they say the word 'pen'. It's the written form that helps us both know what we're saying, as is obvious from the very simple act of saying "How do you spell that?" when you don't understand a word spoken by someone with a different dialect from you. This easy solution, referring to the unifying written form of a word, would be lost with simplified spelling; and when we have to ask someone to describe what they mean, rather than simply spelling it, we are talking about a completely different word from ours, which can mean the difference between two dialects and two languages.
3. The article says of simplified spelling proponents:
They even picket the national spelling bee finals, held every year in Washington, costumed as bumble bees and hoisting signs that say "Enuf is enuf but enough is too much" or "I'm thru with through."
Thae sae th bee selebraets th ability of a fue stoodents to master a dificult sistem that stumps meny utherz hoo cuud do just as wel if speling were simpler.
[To transliterate the last sentence, "They say the bee celebrates the ability of a few students to master a difficult system that stumps many others who could do just as well if spelling were simpler."]
First off: "th ability" ? Why not "the", or even "thee" in this case? And "fue"? Why not "fyu"? Granted, these were written by the reporter, not the proponents of simplified spelling, but I'd love to know what their system will be, because it's bound to have inconsistencies of its own.
Seriously though, the spelling bee isn't just a matter of fabricating a system for a few people to be good at, and then congratulating those few that they're good at it. The reason those talented young spellers are encouraged to be good spellers--and rewarded when they are--is because to be a good speller of English you must study a lot of worthwhile stuff from other languages. In learning the why behind the spellings of many even basic words, those bright young boys and girls learn a lot about Latin, Greek, Old English, German, Hebrew, French, Anglo-Norman, and myriad other languages that have contributed to the language we have today. They also learn rules for how English typically assimilates words from each language. One of the reasons English always seems like it has more exceptions to spelling and pronunciation rules than other languages is because we have multiple sets of rules we're drawing from.
(Note that I'm not talking about syntax, which in English has always been predominantly Germanic, even with non-Germanic vocabulary: Hence "attorneys general" is a construction that English speakers are generally aware of, but that always feels a bit foreign and awkward, hence the tendency to turn it from noun-adjective to compound noun and pluralize it as "attorney generals" (which is still currently grammatically incorrect). Anyway, the native Germanic syntax of English highlights again the absurdity of saying that we shouldn't split infinitives because they weren't split in Latin or some such. If we're going to not split infinitives, it should be for a reason internal to English, and be natural to native speakers, and serve some purpose related to communication: clarity, expressiveness, etc.)
Anyway, the rules of English are definitely complex, especially in America where foreign language are usually taught waaaay too late in school, and English is only taught as having a basic set of rules with a million exceptions, instead of several interacting sets of rules with a more typical amount of exceptions. As a learning tool, though, English can't be beat for what our own native words teach you along the way, and you might try teaching it better before you ditch its historical and international richness.