I do completely agree with the main question of this post...cut all the water shoots.
Trees only have so much energy. Energy put intoArtificially stimulated new growth is energy that can't be put into trunk diameter or food storage or disease/insect defense. Nitrogen will actually stimulate more sucker growth.
The use of 10-10-10 is highly discouraged nowadays as the P is usually unnecessary and simply washed from the soil,leaching into nearby waterways. Some municipalities prohibit any commercial application of fertilizer containing P.
The tree will benefit far more from a natural mulch bed 3" to 4" thick extending to the drip line. No thicker than 4" and not touching the trunk of the tree.
Ya, a lot of tree services offer deep injection fertilizerations. Easy money and so unnecessary as to border on unethical.