And I would disagree with you, good sir, despite the stunning bowtie!
There are most certainly aspects of grammar and usage whose primary purpose is to facilitate clarity and avoid ambiguity, and remaining in step with them assures effective communication. But there are also aspects of informal usage that can serve a rhetorical function within formal writing, and can often serve the communicative intent of the writer or speaker. And that would include starting sentences with “And”.
For example, use of quotations marks around a term that may have multiple connotations can serve to establish an understanding between writer and reader, in the sense of conveying “You understand that I am as doubtful or questioning of this concept or ideological interpretation as you are, right?”. Precision and clarity is not sacrificed in this instance, even though the term does not really require the quotations. If anything, close examination of the roots of literacy in children’s preschool interactions with text through their parents indicates that text is first introduced as conversation, eventually becoming an implied conversation with an understood or imagined conversant, represented by the words on the page. The parent initially serves as proxy for the writer, gradually transferring control to the book/text as the child becomes more able to imagine the writer. Effective writers are cogniscent of that implied conversation and social contract. They obey the Gricean maxims (http://www.glottopedia.de/index.php/Gricean_maxims), and the most enjoyable ones regularly remind the reader that they are there in spirit on the page, if not in body.
FWIW, I make a point of writing in a style very similar to the way I talk, although I suppose that I have a tendency to talk very similarly to the way many people write, so the similarity may not be much of an achievement! Still, people tell me they enjoy what I write, even when it is a report, densely packed with statistics and figures. There should be pleasure in reading; even technical or other serious documents. That doesn’t mean the document has to be frothy and persistently playful or silly. But, it should attempt to enjoy the language, to maintain clarity but occasionally skirt the rules, to introduce more vocabulary when feasible and not too demanding, rather than less, to incorporate the devices of poetry when possible (didja catch that “persistently playful” alliteration a moment ago?), to let the reader savour the sound of things on their tongue and lips, even as they contemplate serious ideas, to draw them in.
I would rather the writer attend to my comprehension first and then my pleasure, so I always want writers to spell accurately and adopt proper usage. But when they have a moment, and the communicative objectives have been met, I am quite open to a little divergence. Jazz musicians have known for a century that you establish the melody first, and THEN you riff off the understood melody and play around it. That doesn’t make it any less musical. The same relationship can exist in good expository writing too. Certainly, commit the rules to memory, and abide by them whenever called for, but be prepared to take a left turn now and then.