YSK it's either "should have" or "should've". "Should of" is incorrect
Why YSK?
The first person who typed "should of" probably heard of it in real life that was meant to be "should've", they typed "should of" online and readers thought that it's grammatically correct to say "should of" which is in fact wrong and it became widespread throughout the years on Reddit.
Not wanting to be purposefully controversial, but language is a tool for communication and as long as it's understood by the target audience, then I'd say it was used effectively.
The English language doesn't have a governing body (unlike say French and Spanish) and so whatever we agree on is correct usage. "Grammatically incorrect" has long been a dog-whistle signifier for elitism (you don't have the expensive education to know what's correct) and racism (the local dialect that you speak isn't our 'prestige' version, therefore you are inferior) and I don't really like to see it. Even when those aren't your intentions when correcting people, it still rankles with me.
Not that I'd write 'should of' on my CV or anything, but it doesn't offend me any on an internet forum.
and as long as it's understood by the target audience
Duy'ou-ndarstend Diz?
Understanding written text is more difficult when the existing established conventions that impart meaning are ignored.
Sure, those conventions evolve over time, some errors are worse than others, and no one's going to write perfectly all the time. But that doesn't mean anything goes and the writer has no responsibility to write clearly and correctly.
True. Just because "language is descriptive" (descriptivist will always let you know) doesn't mean everyone can go freestyle with language, carelessly introducing ambiguity and miscommunication. They always say "as long as it gets the point across" but as a non-native but still pretty fluent, most of the time they don't actually get the point across.
What I'm hearing is we need to set up some kind of formal governing body to properly enforce the grammar rules of English. Maybe Hugo boss could make some uniforms.
It doesn't necessarily have to invoke that kind of imagery. Spanish has the Royal Spanish Academy and within my lifetime they have removed a couple of letters from the alphabet (ch, ll).
I slightly changed my breathing pattern after reading your comment, if that helps. Not full nose-blow-funny, but you caused a small, positive reaction. Keep it up!