With the amount of TLS vulnerabilities I don't really understand why we're not just replacing it completely. From what I've read a lot of the issues is the complexity of the standard itself that we could do much better now that so much more is known about good crypto practice. Google has already pushed HTTP 2 and now 3 thanks to having very sizeable chunks of both the browser and the sites. Why not also have a much b…
If you have the luxury of greenfield development, you are welcome to try this. There's a pretty good chance you'll screw up badly, but regardless when tomorrow more opportunities for mistake are discovered you'll be vulnerable and won't have a greenfield any more. You get to learn basically the same lessons about agility everybody else did, the same way everybody else learned them. Brilliant.
The Web is not a greenfield development. Google may have "pushed HTTP 2" but you can still connect to their sites using HTTP 1.1 because _of course you can_. So that first step, where you throw everything that already exists away, is immediately the end of your whole strategy for the Web or more or less any public Internet service.
You might be thinking. "OK, old crap stuff would be affected, but my new shiny things would be fine". And you're almost right. But you have to really operate a scorched earth policy, the new shiny things _must not_ interoperate with the old crap at all. And that's a deal breaker in practice on the Internet. If you say "Well, if we can't do shiny I guess we'll do the old thing" then you lose immediately, that's the thrust of their TLS 1.3 example, both client and server want to talk TLS 1.3 which isn't vulnerable - but the attacker abuses the fact that they're willing to talk TLS 1.2 instead.
If you don't want to do RSA kex in your own system where you control all servers and clients, don't do RSA kex. I commend this, it's good sense. You can use the exact OpenSSL version described as vulnerable in this article, switch off RSA key exchange entirely at both ends and the vulnerability vanishes. But alas even "almighty" Google does not control all servers and clients on the Web.