Cost effectiveness and use of resources. Let's use your example of a DB system.
You still need hardware to run it all on. That's a "fixed" cost. Using F/OSS won't really change it. You still need a sysadmin/db admin to install/configure/maintain it - that is a "fixed" cost. A fastastic *nix+Postgres guy might cost a little more than a fantastic Windows+MSSQL guy, but not that much different. You still need developers to write code for your product(s) that use your DB system. "Fixed" cost again.
You can pay Microsoft for a license for SQL server, Windows Server to run it on, etc.
Or you can use Linux or BSD with Postgres, Mongo, MySQL, etc. at no license fee/cost. No per user, per cpu, per server, etc. If the CxOs say "but what about support" there are quite a few businesses out there that will do short term (implementation/migration) or per-incident support contracts.
Then the intangibles - no forced upgrades, no worries about product discontinuation, freedom to easily move out of that system and into another, etc