You have just contradicted yourself. If someone is "attempt[ing] to write (phonetically) what [they] think is being said" then they are not being "sloppy". They are doing the best they know how.
I think that is probably rather 'nit-picking'
For a start, as I said, my English teacher would have said that even the words they had mis-heard (e.g. "would've" and "should've") were, themselves, 'sloppy' - and that view would presumably not change if the words were written incorrectly. My point was that many people regard the end-result of what we're talking about as being 'sloppy', and hence probably think that the perpetrator's "best they know" is 'not really good enough' - i.e. they haven't listened carefully enough and/or thought enough about what they are writing.
Having said that, I think that there are some situations in which "the best they know" view is reasonable, and the result therefore fairly understandable/'excusable'. For example, as I said, there have certainly been instances of words that I've only heard (but never seen written) that I have mis-spelled for decades before become aware of my error. Whilst some might say that if I had never seen a word written I should have looked up the spelling before attempting to write it myself, I think it is understandable/excusable that I didn't do that if the spoken word created no suspicion that its written form was not just a simple phonetic representation of the spoken word ('silent letters' are the usual culprit!). This can, of course, be a particular issue with proper nouns, so it's always advisable to check or ask before writing one that one has only ever heard!
Context is always important. When writing a formal document (a manual at work, a CV/application letter, etc), then using 'correct' English is important. When sending a note to a friend (paper / email / text / whatever) then it matters a lot less.
Indeed so, but the 'purists' would often dispute that. The arguments (often involving such people) which arise here often relate to situations in which someone writes something which is technically 'incorrect', but we all "know what they meant". Opinions vary considerably as to how one should react/respond to such a situation.
Having said that, whilst I certainly do not share his blanket opposition to evolution of language (based on the fact that 'evolution' inevitably starts with '{currently} incorrect use of language'), I get as irritated as him (and many others) by some of the language used today - and "should of" etc. comes into that category. Maybe it's partially due to age, and simply 'what we have got used to'. I think I would personally regard some 'evolutions' as being beneficial (sometimes because they represent 'simplifications'), but tend to get irritated when they seem to have been 'pointless' - for example, when I hear my daughters (including the barrister one, who has a first-class degree in English!) using "can I get XYZ?" when asking for something in a shop, or booking a taxi - i simply don't see how that offers any benefit over the 'correct' phraseology!
I'm far less concerned about 'text-speak', when used in text messages, because I regard it simply as a matter of efficiency and expediency. Recent generations may think that they have invented this 'language', but I was brought up, starting well over 50 years ago, using morse code to communicate as a radio amateur, and the 'abbreviated language' (involving few vowels other that "u"!) we used for that would look very familiar to the 'texters' of today! I confess that I do (perhaps irrationally) get irritated when I see 'text-speak being used anywhere
other than in text messages, even in informal e-mails, but maybe that's just me!
Kind Regards, John