You mean for your code, deployed on your systems. Yeah, that works fine.
Now ship a binary to a client system with your static TLS implementation, JPEG decoder, LZ decompressor, whatever. And then go hire someone to watch the CVE feeds every day to know when you have to get them to install an upgrade.
Of, if you don't want it to be your fault when they get pwned, you could just link against the system libraries and tell them to stay updated.
"Static only" makes sense for web apps developed and deployed within the same organization, for embedded solutions where the whole update/upgrade process is known to be under the control of the developer, and... basically nowhere else.
This advice is bad, sorry.