There are pros and cons with both and often it depends on the client / designer. Over the last sixteen years, I’ve created many sites for clients who are not local and all our communications have been online and the occasional phone call.
This is a great way to work if the designer is experienced and if the client is organised. This said, a professional designer can do a great deal to help the client be organised. For example it’s a huge help, and works out better and cheaper for the client, if they can supply all their materials before the build commences.
Another factor is trust. The client has to trust the designer to do the very best job for them. Clients who don’t trust their designer want to be more hands-on so like to use someone local who they feel they can micro-manage. (And they are usually the worst clients!) Clients like these often like to have regular meetings and the designer has to factor this into the cost of the overall project.
But to anyone using a non-professional, I’d suggest using someone local. (Although I’d say always use a pro!)
As you know, I’m based in Florida and over the years have created sites for people in the UK, Japan, Puerto Rico, the Caymans and various places in Europe. It’s easy and works well.
But even when working with local companies, our communication relies mostly on email, texting, Dropbox, Basecamp, password-protected ‘client’s areas’ of their site and various other online facilities. It’s quicker, easier and both parties have a paper trail.