As an American, it's funny to think of our native plants as being invasive in other countries because here we concentrate on non-native invasive plants here such as the African Iris, Kudzu, and Bamboo. Here in Central Texas, lantana is a staple gardening plant. It'll take the winters, the summers, the droughts, the rocky soil, and it'll bloom and grow and look lovely. I have a few kinds in my front garden, and I recently trimmed them back for the upcoming growing season so they can get bushy and lovely. I've even harvested some seeds to see if they'll germinate, and they might... in 180 days or so!
So it's funny/weird to think about this lovely plant being so invasive in Australia and so hated. Looking at list of invasive plants, it's amazing how many of them do well in Central Texas without ever becoming invasive such as prickly pear - here, the deer will eat them as will goats and other hungry quadrupeds.
For the record, I hate mimosas. I dug up over 300 in my small backyard - most were seedlings but there were some with tap roots going down 3 feet or more. My boyfriend and I thought we had to dig out all/most of the root and were for a long time until we realized we could just chop them off just below the soil level. Bah. There are a few people in my neighborhood with mimosa trees. Doom to them. I'm still finding seedlings.