Outlook logon fails after mailbox moves from Exchange 2010 to Exchange 2013 or Exchange 2016

It's the only way, supported and not really an issue if you're aware Ex2013+ caches Autodiscover information. Plan for it, and start your moves with suspend-when-ready. When you are ready to complete the moves, have a script running periodically recycling Autodiscover, OWA and Sync app pools, or lower the recycle interval settings in IIS on those Exchange boxes for those pools.