I disagree on both counts.
We've cleared something like 85% of the native forests/vegetation since settlement. That includes things like mulga and mallee scrub which are tree-ish but rarely more than 4 to 6 metres high.
Also, well dried eucalyptus is my firewood of choice when I go camping, especially redgum. Dense wood, long burn time. Maybe it's different for fireplaces in houses though.