Vic, WA and one other state (sorry can't remember which) learn Vic Modern Cursive if they are following curriculum. Learning running writing is in the Australian Curriculum from (I think) about year 3. So typically they start with the not joined up letters (open b, p, flicks) then start to join later.
Running writing is much faster than printing and most essay exams are still handwritten. (basic answer to OP's question)
Children need to be exposed to texts in many situations (eg. Computer screen, books, signs etc) and part of that is becoming fluent in reading many fonts and linking it to existing letter knowledge. Eg. My 5 year old DD has had to learn that there are two common lower case a's - the circle and stick or the backwards r with a smaller circle under - and that both can be written with tails or not but they are all the same letter. This is all part of learning literacy.
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