I always just rely on the automatic database distribution built-in to Exchange.
If you exclude all the source databases, then it will randomly choose the ones you want:
https://learn.microsoft.com/en-us/exchange/automatic-mailbox-distribution-exchange-2013-help
You can always use a script like this:
Its older yes, written before the automatic stuff was built-in but will still apply:
https://www.allabout365.com/2010/09/balancing-exchange-databases/