J.T.

stump grinding is not essential but it is advisable, it will as Pete says remove a potential habitat for fungi that could go on to colonise other trees who's roots come into contact with the dead stump and it's decaying root system.

Eventually the stump would decay but this may take many years depending on its size, you could leave it and make it a feature of your garden, put some small climbers up it or hollow out the top enough to put some soil and trailing plants in.

You could get the arborist to leave a little or no stump above ground and cover what is left of the stump with mulch, and then plant your herbs around it, though the stump would rot and soil around it would start to subside to fill the cavity left by the decayed wood, you would just have to top the hole up with soil.

Have you spoken to your neighbours on how they feel about removing this tree it is possible they value it for shade and just for its beauty, it's always best to talk to your neighbours to avoid ill feeling or upset.

Plus I’m not sure of the tree protection legislation in Colorado but wont you need a permit to remove this tree? On what grounds will you be able to have it removed if as you say it is not disseised or dead?