I wish there was a FineBuild presentation video. Apparently it has been demonstrated at user groups a lot in the past and yet there's nothing recorded and viewable online that I could find.
My main hesitation with it is that the documentation is so copious, and spread over articles so that it's hard to get a complete picture of what it's doing; some of the wording is vague and it would require lots of time and experimentation to go through the code and work out how to operate it properly and what it's doing underneath the covers.
Up to now though, most DBAs I know have PowerShell written in combination with modifying the configuration files for a semi-automated install. For example we do things like check cluster size of disks, do the install, set up permissions for Hallengren directories, backup directories, grant volume permissions, work out MAXDOP and max server memory, and enable the common trace flags.
There's also Orchestrator runbooks to script installation within System Centre Configuration Manager. But for a DBA who has time to become an SCCM expert just so that you can get it to install something? Especially when your infrastructure department is going to lock you out of it afterwards because you're a mere DBA and not quite on their level. It's a bit of a nightmare.