How much would a db admin charge you per hour to do the same?
I think that's the wrong question.
A better question would be why you don't just rent a $50 dedicated server and run everything, including the database, on that.
If you think you need a "db admin" to do that then you should really re-evaluate your team.
Your $50 database doesn't need that. A simple backup works fine for a great many people.
I don't think your argument holds any merit at the level of hosting costs we talk about.
In order to match the performance of a measly $50/mo dedicated server you'll pay in the ballpark of $1300/mo to Heroku (16GB DB + 16 "dynos"). In between these two figures there's a lot of merit to be had.
have you looked at what is involved in upgrading to say Postgres 9.3 from 9.1
Yes, you stop the db, run pg_upgrade, and start the db.
But as you correctly state, most people in this bracket have no reason to upgrade their database software ever.
Regardless. If you do it yourself you still ned to spend time on it. For most of us that time is not free.