In the end ,,,their tree,,,their money.
I look at it this way.You drive around town,and see an otherwise beautiful home ,painted some weird, and loud non contrasting colors.Doubt the painters wanted to do this to a lovely home,but they have to eat like everybody else.The HO makes the decision,as they have the checkbook.
Pride doesn't pay the bills.
Exactly as I have always said. look at it as job security. You'll be back soon enough to fix or remove the remaining tree.
Another thing to remember is that here in the Northeast, unless you were hit by the ice storms, we haven't had a tree damaging storm for 18 years so the trees have grown unusually tall, normally some of the tall ones would topple over or snap to be repaired later. Some folks top with the intention of safety over looks.