should I remove the carrotwood?

In the backyard of my new home (moving in a few months from now!), there is a large carrotwood tree (C. anacardioides, aka tuckeroo) in the center of the yard. It's a common landscape tree in Southern California because it's decent looking, relatively disease/pest resistant, and quite tolerant to a variety of soil types and water conditions.

Birds love the fruit, and according to the previous owner, the tree often houses various species throughout the year. Negatively, the tree is a non-native invasive (considered noxious in some states), and doesn't produce fruit that people can eat. Moreover, the hard, sharp seed pods make walking barefoot around the tree almost impossible without the utmost care.

Ideally, I'd like a more "productive" (or even more attractive) tree to be the centerpiece of the yard. But for various reasons, part of me feels guilty of cutting down that tree (including that the previous owners planted it and really seem to love that tree, and that matters to me for whatever reason).

I'd love to hear your opinions on this matter! Whether or not I keep that tree is something I feel I should settle before moving on with other plans for the yard. Too bad it has to be right smack dab in the center!

I like carrotwood trees. They are invasive but they are mainly invasive on disturbed spots. They are fast growing, good shade, bring in wildlife, seeds and husks add to the soil. We have them here I have a small one in my yard and still am deciding if I want to keep it. One of the only trees I see that can grow in a stand of casuarinas. I say keep it.

Thanks for the feedback Ichabod!

I say kill it and plant edibles in its place.

Wow! Your situation is almost exactly my situation! We're currently renovating that new house, and will move in this month. The Carrotwood is right in the middle of the backyard and is quite tall. I would also rather have an edible or another hardwood that I am more emotionally connected with (i.e. an Oak or Walnut) and I am loathe to cut it down. It's quite big and has sort of earned it's place in the yard - WE are the interlopers. It could make a good core to a tree house I was thinking of building for my children? I'm a woodworker, and wonder what this orange-colored wood looks like all finished? I will be watching this forum and see what other people think about this too. I'm in Southern California too. Good luck.

Here is South Florida, they are very invasive.  The seeds are distributed by birds who eat the fruits and then defecate them around our neighborhoods.  They grow very quickly, and although they are quite easy to pull up when very small (I'd say up to about 8 inches), they are extremely difficult to pull out if you let them get 1 or 2 feet. To my experience, they have intensive root system: I was digging out and fixing the area behind my fence, in the alley near my oak tree, when I found a shallow root that needed to be removed. I started to pull it out, and it took me all the way to the other side of my yard near my Carrotwood tree, I'd say at least 50". The root is pretty, and orange: I'd say a crafter would find some good use for it. But that is besides the point. Our whole neighborhood is infested by this tree species. It is shifting and damaging fences, it is taking over hedges. I quite often find Carrotwood seedlings trying to grow near the base of my oak tree. I quickly remove them as soon as I see them. There is no weed that draw immediate action from me, as does the Carrotwood seedlings. I would definitely do yourself and your neighbors a favor and cut it down . I have yet to deal with mine. Simply cutting it down won't do because it will sprout up again from the stump. I really like trees, so it is hard for me to say destroy a tree, but for this tree I make an exception. I hope this helps.

Re: treehouse, the branch strength is rated Medium Weak: https://selectree.calpoly.edu/tree-detail/cupaniopsis-anacardioides
We also just bought a house in Southern CA with one of these in the front yard and we are debating cutting it down. I don’t love the way it looks and it also has high biogenic emissions, which contribute to ozone formation.

I hope you cut it down. There are these trees all over my neighborhood– they strangle out other, better trees. They are difficult to get out once grown to about 2 feet, as someone wrote already. I wish everyone in my neighborhood would get rid of them.

I suggest you cut it at pollard height.
Even if it never regrow it can  host life.

Maybe you could prune the tree agressivly and graft somthing more suitable onto whatever is lefties?  
It looks like grafting to carrotwood is not the easiest thing in the world but maybe you can both keep the the original tree and have a new one.
See this link  
https://tropicalfruitforum.com/index.php?topic=8209.0
It

I hate this kind of tree, a lot of seeds spread and grow everywhere, not easy to clean them out, like the seeds the leaves are also very hard, the shape is ugly, I'll spent about $1000 to remove it.