The need for a alternate dbms is entirely dependent on factors such as are you storing attachments or pictures? Are you dealing with millions of records and are approaching the max sizes? Is security of paramount importance? If yes to any of those, then you might need to choose a different back end such as SQL Server or MySql (if it's still around).
If everything is running fine, I would not update from mdb to accdb if that's what you're saying. At most I might update the fe to accdb or accde from mdb/mde.
I suspect your db doesn't use replication otherwise you wouldn't even be able to open it with version 2016. I'll bet there has been a few who found this out the hard way when they updated their version of Office. So I agree, "if it ain't broke, don't fix it".
The more we hear silence, the more we begin to think about our value in this universe.
Paraphrase of Professor Brian Cox.