Historical spellings are the only reason English is still a single language that is mutually intelligible (at least in written form) all around the world. It's the key to its success, not a weakness.
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All versions of English spoken in areas of white native-speaking descent have a very high phonemic similarity. It would not be difficult at all to make a single phonemic spelling that would adequately represent all dialects. There are only a handful of phonemic distinctions that are made only by a minority (WH vs W springs to mind) and even "dropped Rs" are almost never completely dropped.
If we follow your track well we can just look to Latin historically to see what happens. The local street languages will be adapted into faux-literary languages with phonetic spellings, mutually unintelligible.
That's a completely spurious comparison. Latin was spoken by the conquerors, and the locals failed to learn it correctly. The Romance languages show the effects of local language interference (eg intervocalic lenition in Spanish, likely a borrowing from Celtic phonology, insertion of e- at the start of many words in French and Spanish, a borrowing from Basque etc). English is in a completely different situation, because the expansion of the British Empire was concurrent with a population boom triggered by the industrial revolution. This gave a massive surplus population to settle the new colonies. Of course, not every colony got the number of native speakers the US, Australia and New Zealand did. If you look at the Carribean, you'll get creoles arising out of English. Listen to African varieties of English. Or Indian. Or the creoles of Oceania, from the relatively English-like Pitkern and Norfuk to the very exotic, like Bislama. These are the varieties that emerged where native speakers were in the minority -- these are the languages that are analogous to the Romance languages.
So no thank you, let's not try to kill the tongue of Shakespeare. Learn to use it better instead.
Sayest thou that we should cease to use the present progressive...?