Distributions such as CentOS/RHEL which are focused on stability are not going to replace OpenSSL in any existing releases.
I've been testing this against each release for some time and I'm very happy with it.
Note that recently a big clean up of the openssl codebase has taken place so openssl master no longer exposes the internals of structs etc. meaning it's both more auditable and more maintainable. This code is not yet released however.
Many projects have also invested heavily into optimizing the performance of OpenSSL itself or the use of its interfaces.
You can't sprinkle "magic SSL dust" over these components and just start using an alternative. In some cases, significant, non-trivial changes would be required to change which library is used.
The reality is, as fast as OpenSSL development is moving now, it remains the better option for a lot of projects because of the significant investments already being made and concerns I mentioned earlier.
Huh? Of the 22 vulnerabilities OpenSSL has disclosed since March (4 high severity, 14 moderate, 4 low), LibreSSL has been vulnerable to 8 (0 high, 6 moderate, 2 low).
References:
March: https://marc.info/?l=openbsd-cvs&m=142677372515025&w=2
June: https://marc.info/?l=openbsd-announce&m=143406498020131&w=2
Today: https://marc.info/?l=openbsd-tech&m=143645910727507&w=2
See: Exherbo Linux (http://www.exherbo.org/docs/eapi/providers-and-virtuals.html). This isn't one of the big distros, but you do have a choice.