Why do we have “formal” English?

Might be something to do with the roots of the various words or terms.
There are those who maintain that those with Latin or French roots are preferable to those with Germanic origins, and vice versa.

May also have something to do with educational standards?

No doubt most languages have differences between their written and spoken forms. This partly goes with the medium. Written language tends to be more 'careful' and we have a body of precedents to go by. Spoken language, meanwhile, is more spontaneous, friendlier perhaps. And remember it goes both ways: formal language often sounds inappropriate in an informal context. So most of us don't use 'much' and 'many' in positive statements in smonepoken language. We rarely say things like 'I have many ideas' or 'Much time and money has been wasted' in normal spoken language.

What HS says was certainly true in the past but I'm not so sure today. What's more, partly due to email, correspondence for one is getting less formal.

Compared with romance languages, I think English has actually less differences between formal and informal language. Both French and Italian have tenses (especially past simple) that are rarely used in spoken language. Spanish and Italian have 3rd person formal forms while French has 'vous'.

I don't mind so much when the 'caste system' refers to words rather than people. It doesn't particularly bother me using 'many' in more formal writing rather than 'lots of'; while I often use 'lots of' and 'get 'in spoken English, there are times when they don't seem to sound right in more formal language. As with much in language, isn't it simply a case of 'horses for courses'?

But then there are those words like the adverb 'pretty', which I find no problem with, but some others object to in a formal setting.

Sometimes I think that all the things I today forbid in formal writing will some day be considered perfectly acceptable by the generations to come. "Pretty" will be rehabilitated, contractions everywhere, and one-sentence-per-paragraph the norm. Formal English is sometimes just the older generation resisting change.
I have the honour to remain etc...

I can go along with K.I.S.S., but one sentence per paragraph? What would be the point then of paragraphs. Unless each idea is to be expressed in one sentence. And I fear that would sound rather staccato. I think I would prefer a more balanced and varied approach.

Contractions will become more common, certainly, (and I use them on forums such as this), but I doubt in academic language. But not using them in academic work is a convention I can easily live with, although I do warn students that not using them in informal emails can seem stiff or unfriendly.

And it seems obvious to me, that when you want to express more complex ideas, more complex language is going to be needed.

That doesn't mean it has to be old-fashioned, or long-winded. For example, alhough they use some academic language, historians are often excellent writers, partly because they are writing for a more general audience than other disciplines. Or read someone like Steven Pinker, author of 'The Language Instinct' and , more recently, 'The Sense of Style: The Thinking Person's Guide to Writing in the 21st Century'. Academic subject material, yes, contractions, nary a one (I imagine), but clear, easy to read, even a pleasure to read.

Apropos of nothing, I read an article recently suggested banning the word 'amid', because it is ony ever used in print. Well, I like 'amid', and I have noticed that we have quite a lot of words and expressions that tend to be only used in writing (or prepared speech), and this can add to the pleasure of the reader. From an article from the Guardian I've been doing with a student today:

"Out of home advertising has melded itself inextricably into our environment"
"All this sounds rather bucolic, but Grenoblians ... seemed underwhelmed"

Probably not exactly conversational language, but hardly over-fromal. Paragraphs are short, but multi-sentence. (Incidentally, I wonder if the Internet has something to do with it? - Long paragraphs are a pain to read on a computer screen!)

In fact, I think newspapers like the Guardian, The Economist and the NYT get it just about right: neither overformal nor overfamiliar. Perhaps instead of talking about formal and informal, we should talk rather more of 'prepared' and 'spontaneous'. If we wrote exactly as we spoke, I doubt the writing would amount to much, or be much of a pleasure to read.

@WW model English : enjoy!

http://gg.govt.nz/sites/all/files/u2/leaders3_201302151006.pdf

This site seems to go for one-sentence paragraphs much of the time:

http://www.nzherald.co.nz/world/news/article.cfm?c_id=2&objectid=11517471

Either this comes from AFP or someone is deliberately splitting the newsfeed into tiny paragraphs. Whether this splintering improves on-screen readability is a good ask, but it certainly raises questions about the future of paragraphing in general.

Emailing, texting, tweeting--these are already affecting our writing. Remember when you wrote an email like a letter? Now, there is a subtle coercion when someone emails me and hits the carriage return. They are being formal. If they just say hi john and use a hyphen or comma and then start in with whatever they are saying, they are mimicking spoken language, perhaps what you'd expect to hear in a voicemail.

I think we will continue to have formal writing as long as there are business and government transactions. It's authoritarian, I know, but still seems appropriate to me. We are still in the early days of the internet. Wait 20 years, maybe 50. We might see a lot, ahem, much less formal usage.