The point of NIST standardizing on SHA-3 is to gradually replace SHA-2 due to the rise of computing power and the likelihood it will become as weak as SHA-1 is now in the near future. Unfortunately, like American credit cards vs. European chip & pin, it's going to take forever to adopt.
So we need to be careful not to use it in setting where that would be problematic. Or we can use it with workarounds, like double hashing (SHA-256d) or truncating its output.
SHA-3 is sponge based, so its output is always truncated, preventing length-extension attacks. So I think SHA-3 is a better default, though it's fine to use SHA-2 if you know what you're doing.
In a similar manner, apps that verify signatures/certificates often let the certificate specify which algorithm is used, so again effectively an attacker may be able to force the app to use SHA3 as long as it uses a library that has some support for it.
This is a common problem, and massively increases attack surface, since if a vulnerability can be found in any algorithm, it can be exploited. Downgrade attacks are a varient of the same.
Let me present an alternative:
Each protocol has one specific encryption algorithm and set of parameters. However, that set isn't fixed, but defined based on the current date and time.
For example, HTTPS could be defined as "SHA1 from 1996 till 2006", "SHA256 from 2005 till 2018", "SHA3 from 2017 till 2032", etc.
The dates can be written 10+ years into the future, so that software deployed today is still usable that many years into the future. As soon as the last date period expires, the software is not usable until it has been upgraded (unless both ends of the communication link choose to fake the date).
There is precedent for software 'expiring' - that happens whenever the root certificate of a trust store reaches an expiry date.
The downside is sometimes an algorithm might be broken before its date comes, and other times an algorithm may still be secure at that date. But that still seems better than our current mess of downgrade attacks.
Then the release of a new configuration can be done slowly with reasonable caution to get back to the desired redundancy level.
Not necessarily. If the client contacts the server using version X, the server will reply with version X.
Who says that? Either it is specified in the protocol, and then you're right that this is still a negotiation, or it is not specified in the protocol, so if the client does that is implementing some out of spec behavior. Which is true that already happened on the Internet for compatibility's sake, but keep in mind that there is still an advantage, as an adversary can't easily mess in the connection setup phase in a way that protocol version X looks like protocol version Y.
* you expect all servers to upgrade immediately, or at least faster than clients, or
* you delay upgrading clients you know to be insecure until servers had time to upgrade, or
* you are ok with breaking a significant portion of the network for every protocol update.
Either way, your proposal makes no sense for the internet.
Additionally, this is already possible with the current negotiation scheme. You can have clients refuse old algorithms (and they do). Your proposal doesn't improve anything there or anywhere else.
SHA-3 is used extensively within Ethereum contracts and the applications that interact with these contracts. Though, most of these applications are online, (Javascript) and not running C code.
Ethereum currently settles 23 billion a day. It’s probably more financially impactful that it is this hashing algorithm than the equivalent with SHA-2.
edit: Miners might be much more likely to be using it, but I am not familiar with what is used for mining. The actual nodes are in Go though.