See my original post at halfbakery.com, which includes follow-up comments.
The benefits of literate people around the world being able to communicate, regardless of spoken language, are obvious. When building a writing system, there are two possible approaches.
1) Use symbols based on meaning. In such systems there are necessarily a lot of these (in the thousands. Chinese uses this strategy.)
2) Use phonetic values (an alphabet or syllabary). English (and many other non-Roman-alphabet languages) use this system; the number of symbols is often substantially less than 100.
I propose an alphabet, rather than a system of ideograms, and specifically a phonetic version of the Roman alphabet, because
a) well over half of humans live in countries where the Roman alphabet has official or co-official status (3.8 billion)
b) alphabets are easier to learn (if you are a first-language Chinese-speaker and need 3,000 characters to read a newspaper, how hard can it be to learn 30 more?)
The main benefit will be facilitation of second-language learning, rather than universal communication (any monographic alphabet-user learning Japanese or Chinese can attest to this). Because of course different languages have different sounds, an expanded Roman alphabet could be used (mimicking the International Phonetic Alphabet?) That would be more fair, so everyone has to learn a somewhat new system, even people who already read Roman characters.
Someone posted a proposal here that all languages be written in ideograms. Beyond the difficulty of teaching ideograms to alphabet-readers, it's very difficult to adopt these symbols between languages, given differences in word order and grammar. The best-known example, Japanese, uses a klugey system of Chinese characters with home-grown syllabary characters scotch-taping them together within Japanese grammar; and the ideograms do drift from their original meanings, defeating the purpose anyway of adopting such a difficult system.
The problem of implementation is first and foremost a political one, of convincing the Chinese and Arabic-speaking governments of educating their citizenry to be at least bi-scriptural. But Turkey has done so, without which change it's doubtful whether there would even be an argument today over whether they could join the EU. [Added later: it turns out that there were serious proposals in Meiji Japan to Romanize Japanese; they would have beat Ataturk to the punch. There are actually books from this era written in Romanji-Japanese. A study of why it didn't catch on would be informative to this proposal.]