Not only that, you can't just have one DBA. You need a team a them, otherwise that person is going to be on call 24/7, can never take a vacation, etc. Your probably looking at a minimum of 3.
And when you have performance issues you still need a DBA. Because RDS only runs your database. It is up to you to make it fast.
You'll need an engineer with database skills, not a dedicated DBA. I haven't seen a small company with a full time DBA in well over a decade. If you can learn a programming language, you can learn about indexes and basic tuning parameters (buffer pool, cache, etc.)
One of these is not like the others (DBAs are not capex.)
Have you ever considered that if a company can get the same result for the same price ($100K opex for RDS vs same for human DBA), it actually makes much more sense to go the route that takes the human out of the loop?
The human shows up hungover, goes crazy, gropes Stacy from HR, etc.
RDS just hums along without all the liabilities.