That would be neat. I suspect the browser and/or OS would have to be aware of it though, in order to cooperate, in which case why not just have the browser/OS implement it?

With HTTPS it cannot read the URL query params

Not saying it's practical but you could add your own CA on each client device and the router MitMs.

Or, e.g. you can set a flag when building Firefox that will store the secrets necessary to decrypt those packets, and the client sends the secrets to the router which sniffs and decrypts on the fly.

You can, but these sorts of setups have historically been bad about evaluating the upstream certicate/CA chain for validity, and for things like proper certificate transparency.

This might be something a web extension could do, though.