If your trees are healthy and productive I see no reason to do what anyone else says you should. Grass won't 'kill' your trees but it might use some of their water and nutrients. You could compromise and maintain mulched circles around each tree.

Agreed. I'm a big fan of a really thick wood chip layer for paths around the trees. Retains moisture, keeps weeds down. If you want more green, I like planting berry bushes under the trees that benefit from a little shade in my location like currants, gooseberries etc. Just plant em in the soil under the mulch. I'm in KY so summer sun can be a little hard on them without some shade throughout the day.

As long as they get plenty of water grass around your trees will not hurt them. The biggest trees I have are ones with really thick grass around them. They are in a area that gets a lot of water.