You don’t know when the message arrives at the other end. Nor do you know when the reader opens it.
At best ‘good morning’ doesn’t make sense. At worst, it looks rude. It says the writer hasn’t thought about the person at the other end.
This matters if you are in business. An out-of-place ‘good morning’ might be read as “I’m happy to take your money, but I’m too lazy to think about how you might read my email”.
Writers have no control over when people read their emails, so it is best not to start communications that way even when you’re in the same time zone as the reader.
Good morning makes an assumption. If it’s the wrong assumption it can come across as arrogant.
If you want to seem polite or friendly, just start the email with hi or hello followed by the person’s name.
Use the first name if you know them. Use the first and second name if you don’t or if you are uncertain.
Nothing signals the person at the other end is not paying attention more than getting this wrong. If I get an email that starts “Hello Bennett”, I know something odd is going on.
New Zealanders have two better options.
Kia ora is a Māori language – we call it te reo – phrase everyone should know. Strictly speaking it means “good health” but it is widely used as an alternative to “hi”.
The other possibility is g’day – which we share with Australia. It’s a little old-fashioned these days, but serviceable.
Hi, kia ora and g’day have the advantage of working at any time of the day or night. They don’t make presumptions about what is going on at the other end of the communication.