I know that with an all-wheel drive vehicle, you have to keep the tire tread depth about the same. and, if you need to replace a tire when the others are partially worn, you should replace all 4.
But isn’t there an alternative? It should be possible to remove enough tread from the new tire so that it matches the other 3. Can tire dealers do this? Certainly a cheaper alternative, specially if the others are only, say, 1/4 worn.
If not, this is a great idea for a machine to perform this, just shave a few 16ths from tires…