If it was my home I wouldn't remove the tree, but I value mature trees in my garden, not to mention the shade they provide. It's entirely up to you, though.

P.S. Your neighbors really complain about some leaves?

Thank you! Unfortunately, yes, they complain. The furthest branches barely encroach and could be resolved with a trim, minus a small amount of leaves if the wind is blowing that direction. But she has professional lawn maintenance so I was really surprised to be hearing about it. The neighbors have all been pleasant about it, but it's just odd that so many are wanting the tree cut down. There are other oaks in the neighborhood.

Take the oak down now while it is still small. It can not be relocated. Life under a Live Oak is not for someone who is fussy about the lawn or in a neighborhood full of fussy people.

You can replant with palms and smaller ornamental trees like Crape Myrtle, podocarpus, Bottlebrush.

No

The planet is burning up and various people around you want to see an existing tree removed that is currently making a shadow because - like all trees - it generates some litter.

Grasslands show as bare dirt from high altitudes because grass doesn't have enough presence to appear as vegetation. Vegetation that cools, covers and protects.

https://research.noaa.gov/article/ArtMID/587/ArticleID/2742/Despite-pandemic-shutdowns-carbon-dioxide-and-methane-surged-in-2020

Leave the tree.....buy your husband some Claratin for the 2 weeks while the tree is shedding pollen. And pollen and leaves don't kill the grass under an oak tree.....perhaps you need to plant a different kind of grass.
As for the neighbors....tell them to....
But that wouldn't be polite!
And I think the tree is beautifully placed!

Keep it. Remove a circle of grass around the base and put in some ground cover and a bench to relax under the shady tree. Or hang a few bird houses, a feeder, a fountain and enjoy the birds.

No...definitely keep!

The shade it offers is irreplaceable.

Take the oak down now while it is still small. Live oak is a country tree or a city park tree. Live oak is not a tree for your kind neighborhood. If you chose to keep the tree, start an oak tree savings account now. You will need it for the regular LARGE expense of keeping the tree trimmed and limbed up.

This is what happened to Sister #1's builder planted oak 35 years later when the neighbors cut to the lot line because the oak was over their pool enclosure.

Here is a post that shows a Florida backyard and lawn under oak trees.

Landscape Design (houzz.com)

You can plant many more trees to replace the single oak and have a more diverse and interesting landscape.

If you remove the tree, can you add solar panels to your roof? Do you have a source for local, native, wildlife friendly landscaping; and will your HOA approve of such plans.

I agree it's a (blank) shame that some people do not like trees and have no concept of "ecosystem", I better stop typing now!

Much as I hate to lose an oak, I agree with Christopher -- take it down now and replace it with something as nature-friendly as you can get away with. At least you care, unlike some of your neighbors.

Keep the tree. Get rid of the husband and neighbor.

If this tree is still there, I believe it should be removed because it is directly in front of the house, detracting from the house's appearance.

In the first shot the tree is well placed in regard to the house facade. However, the tree is also just big enough to make the house look dinky.

After the oak is removed the exclamation mark fastigiate conifer off the right corner of the house should also be eliminated. Then the house sitting by itself in almost nothing but grass combination that the real estate industry and like-minded clients often think is the only way to go will have been achieved.

If you decide later you want an actual attractive setting with well done landscaping that frames the house and differentiates it from all the more or less lawn-only places that are likely to be nearby then you can always do that then.