There is ongoing debate as to whether the ground under apple trees should be allowed to grow into a grass covering, or cultivated as bare earth.
From experience, generally shrubs and small trees do not grow as well when the grass is allowed to grow right under the tree - up to the trunk,
However, with more established trees then this becomes lees of a problem. Most commercial growers keep the ground under apple trees clean, with a grass 'path' between the rows.
With younger apple trees, if the ground underneath is allowed to grow to grass, then the trees will have to compete with the grass for available nutrients. (The same incidentally, goes for shrubs growing in the lawn.)
There is no doubt, from my own experience, that the ground under apple trees should be kept free from any type of vegetation. A clean area will result in healthier growth, and o course, make it more difficult for many apple tree pests to over-winter there.
In tests carried out by The New York State Agricultural Experiment Station, much larger concentrations of Nitrogen (Food) were found in apple trees where the ground underneath had been controlled by herbicides (weedkillers). This resulted inevitably in better growth for the tree. Additionally, the same study found a greater incidence of over-wintered mites in the soil where the grass had been allowed to grow.
A mulch of organic matter in the autumn is possible with 'clean' soil areas, and this considerably enhances the overall health and well-being of the trees.
The orchard in the image has gone part way to clearing the ground under the young apple trees, but how much more food would be available to the apples if it were not for the lush and greedy grass!
The clearance in this case has barely cleared the outer perimeter of the root growing zone - just where the feeding roots are having to compete with the grass.
The only thing in favour of growing a 'lawn' under fruit trees is the aesthetic appeal of the green grass, and also the convenience of walking on grass rather than soil in damp weather.
Set against that argument, the fact that in virtually any other commercial and gardening growing environment, we do all we can to keep the competition from weeds at a minimum. We certainly don't encourage it, and for good reason!