Is there a market for a secure messaging app (similar to Signal) that does not rely on personally identifying information (phone numbers and emails) or is that too fringe?
Yep. Me too. The network meta-data is always present (IP, src, dst, date, time, etc.). Law enforcement could use that to find criminal actors committing crimes on the app.
But having such an app would allow law abiding individuals to communicate privately and securely without disclosing their personally identifying data to anyone.
Yes. Without an email or phone number there would be no way to do an account recovery, but perhaps some other clever solutions (allow some of your contacts to reset for you, or sign a message with your key, etc.) may be an option.
Now that I'd happily pay for.