I've used Oracle DB and Microsoft SQL Server in the past. I'm using Mysql and Postgresql now and can't say I ever looked at the source code.
While I personally would always use Postgres as first my first choice, I've used both Oracle and SQL Server in various projects in the past. Oracle because we needed to run an application that only supported Oracle, and SQL Server because the company I was working at at the time already had a large SQL Server install. Honestly both are perfectly fine databases and I saw no technical reason to replace either if you already have them. That being said, I didn't have to deal with the licensing or the costs, which are the main arguments against both. Everybody I know who has migrated from Oracle to Postgres has done so, not for technical reasons, but to get away from having to deal with Oracles licensing bullshit.
I would say no but then I am using SQLite which contradicts my statement.
I believe it depends on the project at hand, just like with every dependency/library we use, we barely look at the source code unless the task at hand was mission critical.