(This is a very silly post.)
I was always taught that you start work emails with ‘Dear X’, and that you may perhaps move to ‘Hi X’ if the other party does it first, as a gesture of the connection becoming slightly more intimate over time. Then, if you’re sending multiple emails a day, it’s okay to drop the greeting completely (and sometimes even dropping the sign-off at the end is fine). This is what most of the Britons I email with seem to do; they’re all in on The Rules.
However, I also communicate a lot with Americans over email, and I love the happy jumble of completely informal greetings many of them use.