I have never heard an Australian drop the H in historical though I used to now one old woman who would drop it in herb.
I say 'haitch' instead of 'aitch'. I also say 'hopen' instead of 'open' but I always put that down to the speech defect I had as a child. Certainly most people I know don't do it.
In the 60s & 70s at school in NSW, you could tell which kids transferred fromCAtholic school as they nearly all said "haitch".
Maybe one of my speech therapists went to a Catholic school and I picked it up from her. I had speech therapy from 1963 to 1968, and again for a year or so as a teenager (mainly because as a teenager I was still unable to make the 'th' sound).