Is it weird that this wasn’t in a TPM somewhere? I don’t know how host keys work, are they rotated based on some root cert regularly or is it just the same keypair since the creation of GitHub?
Not really weird, no. The host key needs to be used every time someone establishes a SSH connection to Github. HSMs can't handle that volume of requests.
Given that the key is extremely long lived, this has unfortunate implications: If any of these servers is compromised, or decides to go randomly spewing memory content because of a bitflip, or screws up the nonce on a DSA/ECDSA operation, the key can be compromised. This is hard to exploit if you're a random person, but for a global adversary that collects internet traffic at scale (e.g. NSA), it's feasible and I would be surprised if they weren't exploiting such issues. They were collecting HTTPS handshakes for a reason.
Yes, with ssh you don't use CAs, or certificates at all; just raw asymmetric keys. It does support certificates with all their bells and whistles though, just nobody does really...
Ssh keys are much simpler than the PKI cert infrastructure. This has advantages for development, as well as bug resistance. But it means ssh expects every server behind the same hostname to use the same SSH key.
You can't get two (well functioning) TPMs to have the same key. They come with their own, un-extractable* and unchangeable keys built in.
*TPMs claim this, it is probably not impossible to extract keys just incredibly difficult and requiring specialist knowledge.
There is a diference between the "root" key and the keys you can load into a TPM or HSM. The former is sort of built in, but you can provision several TPM/HSMs with loadable keys and then use those for your crypto implementations - otherwise, every time a TPM/HSM broke, you'd risk data loss.
