On AWS an Aurora RDS is not cheap. But I don't have to spend time or money on an admin.
Is the cost justified? Because that's what cloud is. Not even talking about the level of compliance I get from having every layer encrypted when my hosted box is just a screwdriver away from data getting out the old school way.
When I'm small enough or big enough, self managed makes sense and probably is cheaper. But when getting the right people with enough redundancy and knowledge is getting the expensive part...
But actually - I've never seen this in any if these arguments so far. Probably because actual time required to manage a db server is really unpredictable.