It's about clicks instead of sharing it. So it'll strip it when you click it, instead of copying the link, pasting it, then stripping and hitting enter. Workflow optimization basically :)

Also, more privacy by default seems like a good thing, not everyone understands URLs.

I would like this capability on any home router/cable-modem/FW

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.

Nothing.

I am guessing you never receive links?

It's a convenience feature. Manually cutting parameters out of a huge URL is a pain, and this feature might help to remove that pain. Nothing stops users from continuing to do it manually when they cut and paste URLs.