What are the key differences between regtest and the proposed signet? What are the key differences between regtest and the proposed signet?

One of the key differences is that using regtest is not ideal for public networks as anyone anywhere can just rewrite the blockchain at their whim by mining a ton of blocks. Are there any others?

Is signet a strictly superior replacement to regtest?

If not, when would someone use regtest as opposed to signet in future?
The main difference between signet and regtest is that signet is an actual network, as opposed to a sandboxed environment.
In regtest, the network topology is entirely manual. You spin up nodes, and manually establish connections between them. You have exact control over what blocks are mined and when. This is great for testing things like consensus logic, but it's inconvenient and artificial to use it for testing actual large-scale network effects.
In signet, there is an actual network, with public nodes, operating in a way that's similar to the mainnet network. It doesn't just let you test consensus logic, but also peer discovery, transaction and block propagation, how transactions get selected, ...
Signet doesn't replace regtest; regtest was designed for use in Bitcoin Core automated integration tests and it will continue to be used there. But for other larger-scale tests, of Core and other software, signet(s) may turn out to be a better choice.