Judging from shitloads of successful companies and projects running MySQL in production I'd argue the inability here is with the developer. Can you substantiate your claim or is your dissatisfaction just rooted in your inability to run a MySQL server?
There's several good alternatives - Postgres being free, MS SQL Server being a reasonable paid-for option, and there's Oracle and IBM's database systems at the high end.
One of the only reasons to develop a new project for MySQL (assuming your developers are at all capable of writing queries for Postgres, which is hopefully the case) is that you know your deployment environment is going to have MySQL. Which is probably the case here - LAMP is still a popular stack among PHP developers, so there's a very good chance that anyone wanting to deploy Ghost already has a MySQL server.
Also, big appeal to authority here, many successful companies do silly things with databases.
As a counterpoint, many successful companies run PHP in production but I don't think anyone would claim that means it's a good language.
(One example of where MySQL lack{s,ed}: Postgres with a functional index on a field handled the exact same query on the exact same data a couple of orders of magnitude faster than MySQL on the exact same box.)
After many years of security issues and its general inability to be a good database, I refuse to install it on any of my own boxes. If I need something heavyweight, I'll use Postgres; otherwise it'll be SQLite - both of which manage to be more secure and competent than MySQL.