Draft status or not, it's already going live, at Cloudflare for example, and it won't be long until OpenSSL 1.1.1 comes out with TLS v1.3 support (nginx added support for that yesterday).
SSL handhakes (for HTTPS) are unlikely to be a bottleneck for a web server, even more so now that we have HTTP/2 and various TLS optimizations. If you're looking at "1000 handshakes" (per second?) you're going to run into other bottlenecks first, like bandwidth, a database or disk i/o. Here's a quote from Google, pulled from the site linked above:
On our production frontend machines, SSL/TLS accounts for less than 1% of the CPU load, less than 10 KB of memory per connection and less than 2% of network overhead. Many people believe that SSL/TLS takes a lot of CPU time and we hope the preceding numbers will help to dispel that.
- Adam Langley, Google
I see the benchmark you linked to is actually about adding SSL to MySQL, which is pointless if hosted locally or in a private network, and I think keyplyr was probably referring to adding SSL/TLS to all
web (public-facing) services, HTTP in particular.