My organization is looking at using/favoring Edge because of its integration with o365. Most users currently seem to prefer Chrome, which imports nicely for users manually clicking some prompts in Edge.
To import browser data from Safari to Microsoft Edge in macOS Mojave (yes the KB's a little out of date but it's the most current I could find and it's referenced in the latest install of the browser) you need to allow Edge full disk access via the Security & Privacy prefpane... something we don't like to do. Just for the timeframe in which it's importing the Safari settings, then it can be removed.
If there's a way to swing it this seems like something that could ideally be entirely automated through Self Service for users. One click "import safari history into edge" and be done with it. Something for me to toy with as time allows over the next few weeks, unless someone else solves it for me first.