It'd also be nice to let the current user of your old number to be able to join Signal without issues.
I'd say don't play with fire and migrate as soon as possible before having issues.
You probably could follow https://support.signal.org/hc/en-us/articles/360007062012-Ch...
Then the people with who you discussed on Signal will be notified of your number change. If you can't follow this, better decide to handle it the best way you can instead of having to deal with this when you have lost access.
Basically if someone tries to register to Signal with your phone number they'll need to enter that PIN Signal consistently reminds you of.
You see, if the other person didn't use registration lock, now you've got access to complete strangers account.
Problem solved!
If you view Signal as "a service that allows you to send E2E messages to phone numbers" then this is fine. Your friends will even get a message that says the chat has been rekeyed once the new person sets up Signal.
And if you're worried about government's compelling your cell carrier to turn over your phone number then rest assured that usernames wouldn't help you since they could just compel Signal to turn over your username. So much safer.
As long as the source of identity is something other than a private key that is owned and controlled by the user and devices must have their keys signed by that key to be considered valid it will be the same issue.
I have no respect or interest in using any service which requires a cellphone to use it by fiat.
I don't really have any great concern about the government requesting my information, not because I "don't have anything to hide" or "because I'm too boring to care about" but simply because I don't care if they do. They will do what they will do. I will do what I will do. It's immaterial for me to worry and fret over the actions of someone else. Governments are simply a form of authority which protect those who pay up, and harm those who don't. It's neither my protector or my enemy, it's just a thing that demands money from me from time to time.
As far as secure communications are concerned, if someone is truly concerned about such things, the only reliable method I'm aware of is a one-time pad. [1] For most, such a system would be far too bulky and cumbersome to bother with, meaning that the communication itself is, in actuality, not worth securing to the highest degree. This, in turn, makes the thousands of digital alternatives "good enough" for all but nation-state threat actors. [2]