I'm a professional Landscape Designer in Dallas TX and I've heard for years the controversy about the Mimosa.
Although most of our plant choices for clients tend towards the Native, we also spec adaptive ( native adaptive, ie Crapemyrtles)
And I have used the Albizia julibrissin 'Summer Chocolate' for clients who are true gardeners and have to have a unique plant.
I have the gorgeous Summer Chocolate in my yard ( and young little baby, and expensive too!) - and I love this tree for it's striking bronze/chocolate foliage and pom-pom flowers ( their actually a bit garish for my garden, but they recall wonderful child hood memories)
Here's my 2 cents - yea, it's somewhat invasive and shorter lived than say a Cercis canadensis , but not nearly as troublesome as some plants can be - including natives to north Texas, where I live.
If all you could plant was 1 - 5 trees, then Mimosa wouldn't be in my top recommendations, unless you just had to have a bronze/chocolate foliage tree, as there aren't' many others that I know of.
But if you have a place for a specimen, then go for it! Just know it's kind of messy, so don't put near a pool, and weak wooded
FYI - when it comes to native plants - I have native Horseherb ( Calyptocarpus vialis) that seeded out in my yard - and I can't get rid of it fast enough. If all I wanted was a fast growing ground cover in the shade, this is great, but it over grows everything very fast)