I was speaking to someone a few years ago who used to letterbox with his children and placed about 200 letterboxes on the moor. Once the children had become adults all interest in letterboxing ceased but the boxes were left on the moor.
At least with caching caches can be archived and (hopefully) removed from the moor, but in my opinion too many letterboxes are just left in place after the owner has long lost interest in them.
Well maintained letterboxes and caches should be left in place, but any that are in a bad state and clearly not being cared for should be removed.
I do agree with Dartmoor Dave’s comment that it is up to us all to remove litter when we see it, on our last walk on the moor we picked up a ribena bottle, a milky way wrapper and a mars bar wrapper. Unfortunately litter of all sorts is becoming more common on the moor.