I have a little bit of a hard time believing this: Firefox Addons can use almost all the APIs in the browser that built-in code can, and I'm at least led to believe the new debugging APIs the built-in tools are using are no exception to that rule. https://developer.mozilla.org/en-US/docs/Tools/Debugger-API seems to agree on those points. Or do you mean the tools themselves aren't extensible?

It's been a few years since I've written any Firefox code or touched XPCOM, so I could be looking on this without up-to-date information: I'd be interested if the Firebug authors or others have written any thoughts on struggles they have with this.